Books on the topic '2-category theory'

2-Dimensional Categories provides an introduction to 2-categories and bicategories, assuming only the most elementary aspects of category theory. A review of basic category theory is followed by a systematic discussion of 2-/bicategories; pasting diagrams; lax functors; 2-/bilimits; the Duskin nerve; the 2-nerve; internal adjunctions; monads in bicategories; 2-monads; biequivalences; the Bicategorical Yoneda Lemma; and the Coherence Theorem for bicategories. Grothendieck fibrations and the Grothendieck construction are discussed next, followed by tricategories, monoidal bicategories, the Gray tensor product, and double categories. Completely detailed proofs of several fundamental but hard-to-find results are presented for the first time. With exercises and plenty of motivation and explanation, this book is useful for both beginners and experts.

Monoidal category theory serves as a powerful framework for describing logical aspects of quantum theory, giving an abstract language for parallel and sequential composition and a conceptual way to understand many high-level quantum phenomena. Here, we lay the foundations for this categorical quantum mechanics, with an emphasis on the graphical calculus that makes computation intuitive. We describe superposition and entanglement using biproducts and dual objects, and show how quantum teleportation can be studied abstractly using these structures. We investigate monoids, Frobenius structures and Hopf algebras, showing how they can be used to model classical information and complementary observables. We describe the CP construction, a categorical tool to describe probabilistic quantum systems. The last chapter introduces higher categories, surface diagrams and 2-Hilbert spaces, and shows how the language of duality in monoidal 2-categories can be used to reason about quantum protocols, including quantum teleportation and dense coding. Previous knowledge of linear algebra, quantum information or category theory would give an ideal background for studying this text, but it is not assumed, with essential background material given in a self-contained introductory chapter. Throughout the text, we point out links with many other areas, such as representation theory, topology, quantum algebra, knot theory and probability theory, and present nonstandard models including sets and relations. All results are stated rigorously and full proofs are given as far as possible, making this book an invaluable reference for modern techniques in quantum logic, with much of the material not available in any other textbook.

This chapter provides the topos-theoretic background necessary for understanding the contents of the book; the presentation is self-contained and only assumes a basic familiarity with the language of category theory. The chapter begins by reviewing the basic theory of Grothendieck toposes, including the fundamental equivalence between geometric morphisms and flat functors. Then it presents the notion of first-order theory and the various deductive systems for fragments of first-order logic that will be considered in the course of the book, notably including that of geometric logic. Further, it discusses categorical semantics, i.e. the interpretation of first-order theories in categories possessing ‘enough’ structure. Lastly, the key concept of syntactic category of a first-order theory is reviewed; this notion will be used in Chapter 2 for constructing classifying toposes of geometric theories.

This chapter presents the facsimile of Gerd Faltings' article entitled “A p-adic Simpson Correspondence,” reprinted from Advances in Mathematics 198(2), 2005. In this article, an equivalence between the category of Higgs bundles and that of “generalized representations” of the étale fundamental group is constructed for curves over a p-adic field. The definition of “generalized representations” uses p-adic Hodge theory and almost étale coverings, and it includes usual representations which form a full subcategory. The equivalence depends on the choice of an exponential function for the multiplicative group. The method used in the proofs is the theory of almost étale extensions. A nonabelian Hodge–Tate theory is also developed.

The rabbinic gentile is a minor figure that a minor culture posited as its Other.1 The conditions under which rabbinic communities lived between the first and third centuries minimized the impact this figure could have had on “real” gentiles.2 The goy was a figure who lived in the discourse and imagination of the Judeans who constructed it and reaffirmed it in their everyday practices and was hardly ever adopted by the people to whom the category was assigned. There is simply no evidence that real, actual non-Judeans conceived of themselves as ...

The introduction sets this study in the context of the three recent critical approaches it combines: (1) “metacritical” studies of biblical criticism that identify and critically analyze the “historically effected consciousness” that inspired a particular approach to biblical interpretation; (2) “biographies” of texts that examine their origins and effects; and (3) “end- of” books, which, following the lead of Fukuyama’s “The End of History?” (1989), argue, among other things, that old concepts may fade away as perceptions change. The role of genre methodology in perpetuating the Wisdom Literature category and now in challenging it is introduced. Finally, terminological distinctions are made between the Wisdom Literature category and Wisdom as a genre, the Wisdom Schools associated with it, and wisdom as a concept.

If we assume a Lutheran account of justification as well as the distinction between law and gospel as presented in Chapter 2, the resulting image of God’s activity in the world is a coordinated, twofold action of preservation and redemption. This means we need to add to Chapter 1’s three-act story (creation, fall, redemption) a fourth act: preservation. The theological category of preservation is, for Bonhoeffer, the theological category under which to locate political activity. As this chapter shows, the orientation of Bonhoeffer’s political thought toward preservation distinguishes it from the alternative theo-political visions that he calls “compromise” and “radicalism.” And the main concepts of Bonhoeffer’s political thinking—the two kingdoms and the orders or estates—are ones that structure political life in its preservation toward redemption.

Chapter 2 demonstrates that subjecthood attracted considerable attention from subjects themselves. Indeed, both official and unofficial declarations of rights from the seventeenth and eighteenth centuries popularized British subject status and lent it an almost mythical allure. Declaring and debating rights had a long history in the British world, and the notion that British subjects had inherited and ancient privileges was widely held. Many of these declarations drew on understandings of allegiance and the relationship between subjects and sovereign that echoed legal ones. Their many differences suggest that the rights, liberties, and privileges associated with subject status remained at once limitless and ill-defined. By analyzing a range of declarations, Chapter 2 reveals that subjects of diverse backgrounds had consistently and actively used the relationship between subjects and sovereign to make demands and that subject status, at least in the popular understanding, had been conceived of as a vibrant category of identity well before 1763.

This chapter advances six arguments concerning the relationship between Indian politics and the National Rural Employment Guarantee Act 2005 (NREGA): NREGA, for all its faults, has improved the well-being of tens of millions of poor people; (2) NREGA's political aims and implications must be recognized to appreciate its significance as a development initiative; (3) while the Indian state's porousness provides privileged access to business organizations and socially powerful constituencies, it also offers openings for voices seeking to effect progressive social change in the interests of non-elite groups; (4) various aspects of NREGA implementation have demonstrated the complex process through which “clientelist” politics in India is being transformed rather than eliminated; (5) NREGA is emblematic of a new category of rights—a category we term “governance rights”, which are characterized by hybridity in terms of both content and enforcement mechanisms; and (6) NREGA spurred a devolution of resources to elected local councils, which made village-level democratic institutions, despite their shortcomings, a site where poorer people's demands for accountability were legitimated—a process aided in some states by unusually capable social movements, and in others by state bureaucracies.

This chapter proposes a framework for thinking about the subject matter protectable by intellectual property (IP) and related questions of analytic assistance. The proposed framework is built around certain devices of philosophy, including the artifact, types and tokens, the category, and the property. In combination, these devices support a paradigmatic or focal conception of the subject matter protectable by European and UK IP law. According to that conception, IP subject matter are artifact types distinguished by their properties and categorized accordingly. The analytic and normative value of this conception is discussed, and certain distinctions of importance for IP subject matter outlined, complementing those identified in Chapter 2. The questions of analytic assistance derived from the framework concern the essential properties of IP subject matter, the method of their individuation, their relationship with their concrete instances or tokens, and the manner by which their and their tokens’ existence is known.

This chapter provides further observations, elaboration, demarcation, and application of CEF analysis (and its two foundational pillars of Choice and Equality) as to several key issues and topics of choice-of-law process. In particular, it offers discussion of CEF’s treatment and analysis in the following contexts: (1) CEF’s analysis of the tort law category, including discussion of the centrality of the parties’ reasonable expectations concept, the “conduct regulating”/“loss distribution” distinction, and the experience of the New York Court of Appeal; (2) CEF’s analysis of the lex fori solution to choice of law, including evaluation of Savigny’s rejection of lex-fori and its centrality within choice-of-law practice; (3) CEF’s analysis of so-called “mandatory rules”, including discussion of their origin, popularity, and relation to the party autonomy principle; and (4) CEF’s analysis of the substance-procedure distinction, including discussion of its nature, practice and future direction.

Animal studies is an interdisciplinary field that captures one of the most important topics in contemporary society: how can humans rethink and reconfigure their relationships with other animals? This “animal question” is the focus of The Oxford Handbook of Animal Studies. In the last few decades, animal studies has flourished, with the widespread recognition of (1) the commodification of animals in a wide variety of human contexts, such as the use of animals as food, labor, and objects of spectacle and science; (2) the degradation of the natural world and a staggering loss of animal habitat and species extinction; and (3) the increasing need to coexist with other animals in urban, rural, and natural contexts. These themes are mapped into five major categories, reflected in the titles of the five parts that structure this volume: “Animals in the Landscape of Law, Politics, and Public Policy”; “Animal Intentionality, Agency, and Reflexive Thinking”; “Animals as Objects in Science, Food, Spectacle, and Sport”; “Animals in Cultural Representations”; and “Animals in Ecosystems.” Each category is explicated with specially commissioned chapters written by international scholars from diverse backgrounds, including philosophy, law, history, English, art, sociology, geography, archaeology, environmental studies, cultural studies, and animal advocacy. The thirty chapters of the handbook investigate issues and concepts central to understanding our current relationship with other animals and the potential for coexistence in an ecological community of living beings.

Introduction During the Covid-19 pandemic, non-pharmacological interventions (NPIs) aimed to minimise the spread of the virus as much as possible to avoid the most severe cases and the collapse of health systems. These measures included mobility restrictions in several countries, including Spain. Objective To assess the impact of mobility constraints on incidence, transmission, severe cases and mortality in the evolution of the Covid-19 pandemic. These constraints include: • Mandatory home confinement. • - Recommendation to stay at home. • - Perimeter closures for entry and/or exit from established areas. • - Restriction of night-time mobility (curfew). Methodology Systematic literature review, including documents from official bodies, systematic reviews and meta-analyses. The following reference databases were consulted until October 2021 (free and controlled language): Medline, EMBASE, Cochrane Library, TripDB, Epistemonikos, Royal college of London, COVID-end, COVID-19 Evidence Reviews, WHO, ECDC and CDC. Study selection and quality analysis were performed by two independent researchers. References were filtered firstly by title and abstract and secondly by full text in the Covidence tool using a priori inclusion and exclusion criteria. Synthesis of the results was done qualitatively. The quality of the included studies was assessed using the AMSTAR-II tool. Results The literature search identified 642 studies, of which 38 were excluded as duplicates. Of the 604 potentially relevant studies, 12 studies (10 systematic reviews and 2 official agency papers) were included in the analysis after filtering. One of the official agency papers was from the European Centre for Disease Prevention and Control (ECDC) and the other paper was from the Ontario Agency for Health Promotion and Protection (OHP). The result of the quality assessment with the AMSTAR-II tool of the included systematic reviews was: 3 reviews of moderate quality, 6 reviews of low quality and 1 review of critically low quality. The interventions analysed in the included studies were divided into 2 categories: the first category comprised mandatory home confinement, recommendation to stay at home and curfew, and the second category comprised perimeter blocking of entry and/or exit (local, cross-community, national or international). This division is because the included reviews analysed the measures of mandatory home confinement, advice to stay at home and curfew together without being able to carry out a disaggregated analysis. The included systematic reviews for the evaluation of home confinement, stay-at-home advice and curfew express a decrease in incidence levels, transmission and severe cases following the implementation of mobility limitation interventions compared to the no measure comparator. These conclusions are supported by the quantitative or qualitative results of the studies they include. All reviews also emphasise that to increase the effectiveness of these restrictions it is necessary to combine them with other public health measures. In the systematic reviews included for the assessment of entry and/or exit perimeter closure, most of the studies included in the reviews were found to be modelling studies based on mathematical models. All systematic reviews report a decrease in incidence, transmission and severe case levels following the implementation of travel restriction interventions. The great heterogeneity of travel restrictions applied, such as travel bans, border closures, passenger testing or screening, mandatory quarantine of travellers or optional recommendations for travellers to stay at home, makes data analysis and evaluation of interventions difficult. Conclusions Mobility restrictions in the development of the Covid-19 pandemic were one of the main NPI measures implemented. It can be concluded from the review that there is evidence for a positive impact of NPIs on the development of the COVID-19 pandemic. The heterogeneity of the data from the included studies and their low quality make it difficult to assess the effectiveness of mobility limitations in a disaggregated manner. Despite this, all the included reviews show a decrease in incidence, transmission, hospitalisations and deaths following the application of the measures under study. These measures are more effective when the restrictions were implemented earlier in the pandemic, were applied for a longer period and were more rigorous in their application.

Shortlisted in TAFE Vocational Education category in the 2004 Australian Awards for Excellence in Educational Publishing. The devastation wreaked by bushfires on Australian homes and landscapes is an all too familiar scenario. Yet, why do we often see one house burn, whilst an apparently similar house on an adjacent block can endure? Research has shown that many factors affect the chances of a building surviving a bushfire. If you are designing landscapes and buildings in bushfire areas you need to be aware of these factors so that the chances of losses to life and property can be minimised. Landscape & Building Design for Bushfire Areas integrates the latest scientific knowledge about buildings and bushfires with a flexible design approach. The book contains two main sections: 1) Provides a clear description of what happens in a bushfire. It describes the environment in which bushfires occur, how a fire attacks, and how buildings are ignited and destroyed. 2) Sets out a practical design approach to the design of buildings and their immediate surroundings. It presents a range of options for designing the various elements of both landscapes and buildings in bushfire-prone areas. This book encourages design for bushfire to be included as a normal part of designing in bushfire-prone areas, rather than as an undesirable add-on. It will assist planning and building regulatory authorities to improve and administer regulatory requirements and guidelines.

An analysis of the existing literature on the issue of damage to regeneration caused by timber harvesting, revealed that a great majority of results reported in those publications was obtained through laborious and time-consuming field research conducted in two stages. Field research methods for gathering data, employed by various authors, differed in terms of the manner of establishing trial plots, the accuracy of counting and evaluating the number of saplings growing on the investigated sites, classification systems used for distinguishing particular groups of regeneration based on quantitative (diameter at breast height, tree height) and qualitative features (biosocial position within the certain layer and the entire stand), classification systems used for identifying types of damage caused by cutting and felling, as well as transporting operations, and finally the duration of observation intervals and time spent on gathering data on the response of damaged saplings from both, the individual and collective perspectives. Obviously, the most reliable manner of gathering such data would be to count all damaged elements of the environment being a subject of interest of particular investigators at the certain point of time. However, due to time and work consumption of this approach, which is besides very costly, any research should be designed in such a manner as to reduce the above-mentioned factors. This paper aimed to (1) analyse the probability of occurrence of damage to regeneration depending on the form of timber assortments dragged from the felling site to the skidding routes, and timber harvesting technology employed in logging works, and (2) identify a method ensuring that gathered data is sufficient for performing reliable evaluation of share of damage to regeneration at acceptable accuracy level, without necessity to establish trial plots before commencing harvesting works. The scope of these studies enclosed a comparison between two motor-manual methods of timber harvesting in thinned stands, with dragging of timber in the first stage of skidding from the stand to landings. According to one of these methods, a classical one, operations of felling and delimbing of trees were carried out by sawmen at the felling site. Timber obtained using different methods was skidded by carters and horses, and operators of a light-duty cable winch, driven by the chainsaw’s engine, as well as operators of cable winches combined with farm tractors. In the latter, alternative method, sawmen performed only cutting and felling of trees. Delimbing and cross-cutting of trunks, dragged from the felling sites, was carried out by operators of processors combined with farm tractors, worked on skidding routes. The research was conducted in the years 2002–2010 in stands within the age classes II–IV mostly, located in the territories of Regional Directorates of State Forests in Krakow and Katowice, and in the Forest Experimental Unit in Krynica-Zdrój. In the course of a preliminary stage of investigations 102 trial plots were established in stands within early and late tinning treatments. As a result of the field research carried out in two stages, more than 3.25 thsd. circular sites were established and marked, on the surface of which over 25 thsd. saplings constituting the regeneration layer were inventoried. Based on the results of investigations and analyses it was revealed that regardless of the category of thinning treatment, the highest probability of occurrence of destroying P(ZN) to regeneration (0.24–0.44) should be expected when the first stage of timber skidding is performed using cable winches. Slightly lower values of probability (0.17–0.33) should be expected in stands where timber is skidded by horses, while in respect to processor-based skidding technology the probability of destroying occurrence oscillates between 0.12 and 0.27, depending on the particular layer of regeneration. P(ZN) values, very close to those of skidding technology engaging processors, were recorded for skidding performed using the light-duty cable winch driven by the chainsaw’s engine (0.16–0.27). The highest probability of damage P(USZK) to regeneration (0.16–0.31) can be expected when processors are used in the first stage of timber skidding. Slightly lower values of probability (0.14–0.23) were obtained when skidding was performed with the use of cable winches, whereas engaging horses for hauling of trunks results in probability of damage occnrrence oscillating between 0.05–0.20, depending on the particular layer of regeneration. With regard to the probability of occurrence of both, destroying and damage P(ZNUSZK) to regeneration (0.33–0.54), the highest values can be expected when cable winches are engaged in the first stage of skidding. Little lower (0.30–0.43) was the probability of their occurrence if processor-based technology of skidding was employed, while in respect to horse skidding these values oscillated between 0.27–0.41, depending on the layer of regeneration. The lowest values of probability of occurrence of damage P(USZK), and destroying and damage treated collectively P(ZNUSZK), within all layers of regeneration, were recorded in stands where thinning treatments were performed using the light-duty cable winch driven by the chainsaw’s engine. The models evaluated and respective equations, developed based on those models, for evaluating the number of destroyed saplings ZNha (tab. 40, 42, 44, 46, 48) could be used for determining the share of damage expressed as a percentage, upon conducting only one field research at the investigated felling sites, once the timber harvesting and skidding would have been completed. As revealed by the results of analyses, evaluation of statistically significant regression models was possible for all layers of regeneration (tab. 39, 41, 43, 45, 47). Nevertheless, the smallest part of these models that could be considered positively verified, were those for the natural young regeneration, although almost a half of them revealed to be significant. Within the medium-sized regeneration over three-fourths of all models could be considered positively verified, four of which explained more than 50% of variability. Within the high-sized regeneration almost two-thirds of evaluated regression models were statistically significant, five of which were verified positively, moreover, one of them explained more than 50% of variability. The most promising results were those obtained for the advance growth. Nearly 90% of the evaluated models revealed to be statistically significant, ten of which could be considered positively verified. Furthermore, four statistically significant models explained over 50% of general variability. With regard to the entire regeneration more than 80% of evaluated models were statistically significant. However, due to insignificant coefficients of regression, eight of them could be considered positively verified. At this point it should be stressed that in respect to logging technology employing the light-duty cable winch FKS it was impossible to evaluate statistically significant models of regression. Whereas, in the case of processor-based logging technology, firstly regarding the advance growth, and then the entire regeneration, all of the evaluated statistically significant models could be considered positively verified, in terms of both, all of the stands, and particular categories of thinning treatments individually. This latter case also revealed the highest degree of matching of evaluated models (R2 popr 0.73–0.76 for advance growth and 0.78–0.94 for the entire regeneration). A significant impact of the kind of form of hauled timber on the probability of damage occurrence P(USZK), mainly in early thinning treatments, could have been reflected in the results obtained for all stands (early and late thinning treated collectively). Moreover, due to an insignificant impact of the form of hauled timber and logging technology employed, on the probability of occurrence of damage in late thinned stands, and a significant impact of the above-mentioned variables on early thinned stands, it should be assumed that for performing an evaluation of destroying and damage caused by timber harvesting the both thinning treatment categories should be analysed separately. Furthermore, when evaluating the probability of occurrence of destroying and damage caused by timber harvesting, the layers of natural young regeneration and advance growth should be analysed separately. As proved by the results presented in this paper, varying values of probability computed for each of the layers of regeneration seem to indicate that when investigating damage to regeneration caused by timber harvesting, it would be reasonable and recommended to perform a separate analysis of damage to the highest saplings as well, namely individuals with diameter at breast height close to 7 cm. In respect to studies on damage to regeneration caused by logging technologies mentioned above, the evaluation of number of destroyed saplings within the advance growth can be carried out using the proportions of damaged and undamaged saplings per 1 ha of the stand. The numbers evaluated in this manner can be used to calculate the damage share expressed in relative values (percentage of damaged saplings compared with the entire number of saplings before commencing the logging works). However, one should keep in mind that this is true only if the field research have been carried out based on the methodology described in this paper.