Дисертації з теми "Monoidal structures"
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Espalungue, d'Arros Sophie d'. "Operads in 2-categories and models of structure interchange." Electronic Thesis or Diss., Université de Lille (2022-....), 2023. http://www.theses.fr/2023ULILB053.
The goal of this thesis is to give an effective construction of a cofibrant resolution of the Balteanu-Fiedorowicz-Schwänzl-Vogt operads M_n, which govern iterated monoidal categories.In a first part of the thesis, we study thoroughly the definition of monoidal structures in 2-categories, and the definition of operads in monoidal 2-categories, with the 2-category of categories as a main motivating example. Then we prove that the category of operads in the category of small categories inherits a model structure by transfer of the folk model structure on the category of small categories. We introduce a notion of polygraphic presentation of operads in the category of small categories in order to define operads with generators and relations in both the operadic direction and the categorical direction at the morphism level. We revisit the definition of the operads M_n in terms of polygraphic presentations, and we gives a presentation of an operad M_1^infinity that provides a cofibrant resolution of the operad M_1 in the folk modelstructure. Eventually, we study a generalization of the Boardman-Vogt tensor product in the context of operads in the category of small categories. We use this construction to provide a cofibrant resolution M_n^infinity of the operad M_n from the resolution M_1^infinity of M_1, and hence, to address the initial question of the thesis
Reischuk, Rebecca [Verfasser]. "The monoidal structure on strict polynomial functors / Rebecca Reischuk." Bielefeld : Universitätsbibliothek Bielefeld, 2016. http://d-nb.info/110564555X/34.
Staten, Corey. "Structure diagrams for symmetric monoidal 3-categories: a computadic approach." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1525455392722049.
Aquilino, Cosima [Verfasser]. "On strict polynomial functors: monoidal structure and Cauchy filtration / Cosima Aquilino." Bielefeld : Universitätsbibliothek Bielefeld, 2016. http://d-nb.info/110754064X/34.
Kunhardt, Walter. "On infravacua and the superselection structure of theories with massless particles." Doctoral thesis, [S.l.] : [s.n.], 2001. http://deposit.ddb.de/cgi-bin/dokserv?idn=962816159.
Aquilino, Cosima [Verfasser]. "On strict polynomial functors: monoidal structure and Cauchy filtration. (Ergänzte Version) / Cosima Aquilino." Bielefeld : Universitätsbibliothek Bielefeld, 2016. http://nbn-resolving.de/urn:nbn:de:hbz:361-29054451.
Li, Zhuo. "Orbit structure of finite and reductive monoids." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq21301.pdf.
Zeng, William J. "The abstract structure of quantum algorithms." Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:cace8fba-b533-42f7-b9fd-959f2412c2a7.
Emtander, Eric. "Chordal and Complete Structures in Combinatorics and Commutative Algebra." Doctoral thesis, Stockholms universitet, Matematiska institutionen, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-48241.
Gay, Joël. "Representation of Monoids and Lattice Structures in the Combinatorics of Weyl Groups." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS209/document.
Algebraic combinatorics is the research field that uses combinatorial methods and algorithms to study algebraic computation, and applies algebraic tools to combinatorial problems. One of the central topics of algebraic combinatorics is the study of permutations, interpreted in many different ways (as bijections, permutation matrices, words over integers, total orders on integers, vertices of the permutahedron…). This rich diversity of perspectives leads to the following generalizations of the symmetric group. On the geometric side, the symmetric group generated by simple transpositions is the canonical example of finite reflection groups, also called Coxeter groups. On the monoidal side, the simple transpositions become bubble sort operators that generate the 0-Hecke monoid, whose algebra is the specialization at q=0 of Iwahori’s q-deformation of the symmetric group. This thesis deals with two further generalizations of permutations. In the first part of this thesis, we first focus on partial permutations matrices, that is placements of pairwise non attacking rooks on a n by n chessboard, simply called rooks. Rooks generate the rook monoid, a generalization of the symmetric group. In this thesis we introduce and study the 0-Rook monoid, a generalization of the 0-Hecke monoid. Its algebra is a proper degeneracy at q = 0 of the q-deformed rook monoid of Solomon. We study fundamental monoidal properties of the 0-rook monoid (Green orders, lattice property of the R-order, J-triviality) which allow us to describe its representation theory (simple and projective modules, projectivity on the 0-Hecke monoid, restriction and induction along an inclusion map).Rook monoids are actually type A instances of the family of Renner monoids, which are completions of the Weyl groups (crystallographic Coxeter groups) for Zariski’s topology. In the second part of this thesis we extend our type A results to define and give a presentation of 0-Renner monoids in type B and D. This also leads to a presentation of the Renner monoids of type B and D, correcting a misleading presentation that appeared earlier in the litterature. As in type A we study the monoidal properties of the 0-Renner monoids of type B and D : they are still J-trivial but their R-order are not lattices anymore. We study nonetheless their representation theory and the restriction of projective modules over the corresponding 0-Hecke monoids. The third part of this thesis deals with different generalizations of permutations. In a recent series of papers, Châtel, Pilaud and Pons revisit the algebraic combinatorics of permutations (weak order, Malvenuto-Reutenauer Hopf algebra) in terms of the combinatorics of integer posets. This perspective encompasses as well the combinatorics of quotients of the weak order such as binary trees, binary sequences, and more generally the recent permutrees of Pilaud and Pons. We generalize the weak order on the elements of the Weyl groups. This enables us to describe the order on vertices of the permutahedra, generalized associahedra and cubes in the same unified context. These results are based on subtle properties of sums of roots in Weyl groups, and actually fail for non-crystallographic Coxeter groups
Owusu-Mensah, Isaac. "Algebraic Structures on the Set of all Binary Operations over a Fixed Set." Ohio University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1584490788584639.
Karaboghossian, Théo. "Invariants polynomiaux et structures algébriques d'objets combinatoires." Thesis, Bordeaux, 2020. http://www.theses.fr/2020BORD0123.
In the first half of this dissertation, we study the polynomial invariants defined by Aguiar and Ardila in arXiv:1709.07504 in the context of Hopf monoids. We first give a combinatorial interpretation of these polynomials over the Hopf monoids of generalized permutahedra and hypergraphs in both non negative and negative integers. We then use them to deduce similar interpretation on other combinatorial objects(graphs, simplicial complexes, building sets, etc).In the second half of this disseration, we propose a new way of defining and studying operads on multigraphs and similar objects.We study in particular two operads obtained with our method. The former is a direct generalization of the Kontsevich-Willwacher operad.This operad can be seen as a canonical operad on multigraphs,and has many interesting suboperads.The latter operad is a natural extension of the pre-Lie operad in a sense developed here and it is related to the multigraph operad. We also present various results on some of the finitely generated suboperads of the multigraph operad and establish links between them and the commutative operad and the commutative magmatic operad
Chamboredon, Jérémy. "Algorithmique des tresses et de l’autodistributivité." Caen, 2011. http://www.theses.fr/2011CAEN2016.
In this work, we investigate algebraic properties for Artin's braid groups and self-distributive systems on the left, two objets which are linked. The first part is a syntactic analysis of Bressaud's normal formal for braids. The principal result is a translation in terms of rewriting systems of the existence of Bressaud's normal form, initially established by geometric methods. The second part deals with the embedding conjecture for self-distributivity, one of the principal open statements of the field. We discuss the various ways (including the computing ones) which could lead to this conjecture, and we establish some partial positive results
Maja, Pech. "Local methods for relational structures and their weak Krasneralgebras." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2009. http://dx.doi.org/10.2298/NS20090522PECH.
U ovoj tezi su razvijene lokalne metode koje se mogu koristiti za izu-ˇcavanje unarnih delova klonova (ili, ekvivalentno, slabih Krasnerovih algebri).Koriˇs´cenjem jezika teorije modela i Galoovih veza uspostavljen je odnos izmeduhomomorfizam-homogenih relacionih struktura i lokalnih metoda, preko pojmaendolokalnosti. Dobijeni teoretski rezultati su upotrebljeni za razvoj sistematsketeorije za klasifikaciju homomorfizam-homogenih struktura.
McPhee, Jillian Dawn. "Endomorphisms of Fraïssé limits and automorphism groups of algebraically closed relational structures." Thesis, University of St Andrews, 2012. http://hdl.handle.net/10023/3358.
Slama, Franck. "Automatic generation of proof terms in dependently typed programming languages." Thesis, University of St Andrews, 2018. http://hdl.handle.net/10023/16451.
[Verfasser], Apirat Wanichsombat. "Algebraic structure of endomorphism monoids of finite graphs / von Apirat Wanichsombat." 2011. http://d-nb.info/1012674908/34.
[Verfasser], Somnuek Worawiset. "The structure of endomorphism monoids of strong semilattices of left simple semigroups / von Somnuek Worawiset." 2011. http://d-nb.info/1012672573/34.
Peterson, Clayton. "Analyse de la structure logique des inférences légales et modélisation du discours juridique." Thèse, 2014. http://hdl.handle.net/1866/11159.
La présente thèse fait état des avancées en logique déontique et propose des outils formels pertinents à l'analyse de la validité des inférences légales. D'emblée, la logique vise l'abstraction de différentes structures. Lorsqu'appliquée en argumentation, la logique permet de déterminer les conditions de validité des inférences, fournissant ainsi un critère afin de distinguer entre les bons et les mauvais raisonnements. Comme le montre la multitude de paradoxes en logique déontique, la modélisation des inférences normatives fait cependant face à divers problèmes. D'un point de vue historique, ces difficultés ont donné lieu à différents courants au sein de la littérature, dont les plus importants à ce jour sont ceux qui traitent de l'action et ceux qui visent la modélisation des obligations conditionnelles. La présente thèse de doctorat, qui a été rédigée par articles, vise le développement d'outils formels pertinents à l'analyse du discours juridique. En première partie, nous proposons une revue de la littérature complémentaire à ce qui a été entamé dans Peterson (2011). La seconde partie comprend la contribution théorique proposée. Dans un premier temps, il s'agit d'introduire une logique déontique alternative au système standard. Sans prétendre aller au-delà de ses limites, le système standard de logique déontique possède plusieurs lacunes. La première contribution de cette thèse est d'offrir un système comparable répondant au différentes objections pouvant être formulées contre ce dernier. Cela fait l'objet de deux articles, dont le premier introduit le formalisme nécessaire et le second vulgarise les résultats et les adapte aux fins de l'étude des raisonnements normatifs. En second lieu, les différents problèmes auxquels la logique déontique fait face sont abordés selon la perspective de la théorie des catégories. En analysant la syntaxe des différents systèmes à l'aide des catégories monoïdales, il est possible de lier certains de ces problèmes avec des propriétés structurelles spécifiques des logiques utilisées. Ainsi, une lecture catégorique de la logique déontique permet de motiver l'introduction d'une nouvelle approche syntaxique, définie dans le cadre des catégories monoïdales, de façon à pallier les problèmes relatifs à la modélisation des inférences normatives. En plus de proposer une analyse des différentes logiques de l'action selon la théorie des catégories, la présente thèse étudie les problèmes relatifs aux inférences normatives conditionnelles et propose un système déductif typé.
The present thesis develops formal tools relevant to the analysis of legal discourse. When applied to legal reasoning, logic can be used to model the structure of legal inferences and, as such, it provides a criterion to discriminate between good and bad reasonings. But using logic to model normative reasoning comes with some problems, as shown by the various paradoxes one finds within the literature. From a historical point of view, these paradoxes lead to the introduction of different approaches, such as the ones that emphasize the notion of action and those that try to model conditional normative reasoning. In the first part of this thesis, we provide a review of the literature, which is complementary to the one we did in Peterson (2011). The second part of the thesis concerns our theoretical contribution. First, we propose a monadic deontic logic as an alternative to the standard system, answering many objections that can be made against it. This system is then adapted to model unconditional normative inferences and test their validity. Second, we propose to look at deontic logic from the proof-theoretical perspective of category theory. We begin by proposing a categorical analysis of action logics and then we show that many problems that arise when trying to model conditional normative reasoning come from the structural properties of the logic we use. As such, we show that modeling normative reasoning within the framework of monoidal categories enables us to answer many objections in favour of dyadic and non-monotonic foundations for deontic logic. Finally, we propose a proper typed deontic system to model legal inferences.