Добірка наукової літератури з теми "Grothendieck fibration"
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Статті в журналах з теми "Grothendieck fibration"
Morone, Flaviano, Ian Leifer, and Hernán A. Makse. "Fibration symmetries uncover the building blocks of biological networks." Proceedings of the National Academy of Sciences 117, no. 15 (March 31, 2020): 8306–14. http://dx.doi.org/10.1073/pnas.1914628117.
Повний текст джерелаMARCOLLI, MATILDE, and JESSICA SU. "ARITHMETIC OF POTTS MODEL HYPERSURFACES." International Journal of Geometric Methods in Modern Physics 10, no. 04 (March 6, 2013): 1350005. http://dx.doi.org/10.1142/s0219887813500059.
Повний текст джерелаJOHNSON, MICHAEL, ROBERT ROSEBRUGH, and R. J. WOOD. "Lenses, fibrations and universal translations." Mathematical Structures in Computer Science 22, no. 1 (September 19, 2011): 25–42. http://dx.doi.org/10.1017/s0960129511000442.
Повний текст джерелаT., Pirasgvili. "Category of eilenberg - maclane fibrations and cohomology of grothendieck constructions." Communications in Algebra 21, no. 1 (January 1993): 309–41. http://dx.doi.org/10.1080/00927879208824563.
Повний текст джерелаBalzin, Edouard. "Derived Sections of Grothendieck Fibrations and the Problems of Homotopical Algebra." Applied Categorical Structures 25, no. 5 (January 28, 2017): 917–63. http://dx.doi.org/10.1007/s10485-017-9483-1.
Повний текст джерелаZhang, Yeping. "A Riemann–Roch–Grothendieck theorem for flat fibrations with complex fibers." Comptes Rendus Mathematique 354, no. 4 (April 2016): 401–6. http://dx.doi.org/10.1016/j.crma.2016.01.011.
Повний текст джерелаHe, Yang-Hui, John McKay, and James Read. "Modular subgroups, dessins d’enfants and elliptic K3 surfaces." LMS Journal of Computation and Mathematics 16 (2013): 271–318. http://dx.doi.org/10.1112/s1461157013000119.
Повний текст джерелаMahadevan, Sridhar. "Universal Causality." Entropy 25, no. 4 (March 27, 2023): 574. http://dx.doi.org/10.3390/e25040574.
Повний текст джерелаStenzel, Raffael. "On notions of compactness, object classifiers, and weak Tarski universes." Mathematical Structures in Computer Science, February 20, 2023, 1–18. http://dx.doi.org/10.1017/s0960129523000051.
Повний текст джерелаRandal-Williams, Oscar. "The family signature theorem." Proceedings of the Royal Society of Edinburgh: Section A Mathematics, January 18, 2023, 1–44. http://dx.doi.org/10.1017/prm.2022.91.
Повний текст джерелаДисертації з теми "Grothendieck fibration"
Balzin, Eduard. "Les fibrations de Grothendieck et l’algèbre homotopique." Thesis, Nice, 2016. http://www.theses.fr/2016NICE4032/document.
Повний текст джерелаThis thesis is devoted to the study of families of categories equipped with a homotopical structure. The principal results comprising this work are:i. A generalisation of the Reedy model structure, which, in this work, is constructed for sections of a suitable family of model categories over a Reedy category. Unlike previous considerations, such as Hirschowitz-Simpson, we require as little as possible from the family, so that our result may be applied in situations when the transition functors in the family are non-linear in nature. ii. An extension of Segal formalism for algebraic structures to the setting of monoidal categories over an operator category in the sense of Barwick. We do this by treating monoidal structures using the language of Grothendieck opfibrations, and introduce derived sections of the latter using the simplicial replacements of Bousfield-Kan. Our Reedy structure result then permits to work with derived sections. iii. A proof of a certain homotopy descent result, which gives sufficient conditions on when an inverse image functor is an equivalence between suitable categories of derived sections. We show this result for functors which satisfy a technical ``Quillen Theorem A''-type property, called resolutions. One example of a resolution is given by a functor from the category of planar marked trees of Kontsevich-Soibelman, to the stratified fundamental groupoid of the Ran space of the $2$-disc. An application of the homotopy descent result to this functor gives us a new proof of Deligne conjecture, providing an alternative to the use of operads
Cagne, Pierre. "Towards a homotopical algebra of dependent types." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC063/document.
Повний текст джерелаThis thesis is concerned with the study of the interplay between homotopical structures and categorical model of Martin-Löf's dependent type theory. The memoir revolves around three big topics: Quillen bifibrations, homotopy categories of Quillen bifibrations, and generalized tribes. The first axis defines a new notion of bifibrations, that classifies correctly behaved pseudo functors from a model category to the 2-category of model categories and Quillen adjunctions between them. In particular it endows the Grothendieck construction of such a pseudo functor with a model structure. The main theorem of this section acts as a charaterization of the well-behaved pseudo functors that tolerates this "model Gothendieck construction". In that respect, we improve the two previously known theorems on the subject in the litterature that only give sufficient conditions by designing necessary and sufficient conditions. The second axis deals with the functors induced between the homotopy categories of the model categories involved in a Quillen bifibration. We prove that this localization can be performed in two steps, by means of Quillen's construction of the homotopy category in an iterated fashion. To that extent we need a slightly larger framework for model categories than the one originally given by Quillen: following Egger's intuitions we chose not to require the existence of equalizers and coequalizers in our model categories. The background chapter makes sure that every usual fact of basichomotopical algebra holds also in that more general framework. The structures that are highlighted in that chapter call for the design of notions of "homotopical pushforward" and "homotopical pullback". This is achieved by the last axis: we design a structure, called relative tribe, that allows for a homotopical version of cocartesian morphisms by reinterpreting Grothendieck (op)fibrations in terms of lifting problems. The crucial tool in this last chapter is given by a relative version of orthogonal and weak factorization systems. This allows for a tentative design of a new model of intentional type theory where the identity types are given by the exact homotopical counterpart of the usual definition of the equality predicate in Lawvere's hyperdoctrines
Weighill, Thomas. "Bifibrational duality in non-abelian algebra and the theory of databases." Thesis, Stellenbosch : Stellenbosch University, 2014. http://hdl.handle.net/10019.1/96125.
Повний текст джерелаENGLISH ABSTRACT: In this thesis we develop a self-dual categorical approach to some topics in non-abelian algebra, which is based on replacing the framework of a category with that of a category equipped with a functor to it. We also make some first steps towards a possible link between this theory and the theory of databases in computer science. Both of these theories are based around the study of Grothendieck bifibrations and their generalisations. The main results in this thesis concern correspondences between certain structures on a category which are relevant to the study of categories of non-abelian group-like structures, and functors over that category. An investigation of these correspondences leads to a system of dual axioms on a functor, which can be considered as a solution to the proposal of Mac Lane in his 1950 paper "Duality for Groups" that a self-dual setting for formulating and proving results for groups be found. The part of the thesis concerned with the theory of databases is based on a recent approach by Johnson and Rosebrugh to views of databases and the view update problem.
AFRIKAANSE OPSOMMING: In hierdie tesis word ’n self-duale kategoriese benadering tot verskeie onderwerpe in nie-abelse algebra ontwikkel, wat gebaseer is op die vervanging van die raamwerk van ’n kategorie met dié van ’n kategorie saam met ’n funktor tot die kategorie. Ons neem ook enkele eerste stappe in die rigting van ’n skakel tussen hierdie teorie and die teorie van databasisse in rekenaarwetenskap. Beide hierdie teorieë is gebaseer op die studie van Grothendieck bifibrasies en hul veralgemenings. Die hoof resultate in hierdie tesis het betrekking tot ooreenkomste tussen sekere strukture op ’n kategorie wat relevant tot die studie van nie-abelse groep-agtige strukture is, en funktore oor daardie kategorie. ’n Verdere ondersoek van hierdie ooreemkomste lei tot ’n sisteem van duale aksiomas op ’n funktor, wat beskou kan word as ’n oplossing tot die voorstel van Mac Lane in sy 1950 artikel “Duality for Groups” dat ’n self-duale konteks gevind word waarin resultate vir groepe geformuleer en bewys kan word. Die deel van hierdie tesis wat met die teorie van databasisse te doen het is gebaseer op ’n onlangse benadering deur Johnson en Rosebrugh tot aansigte van databasisse en die opdatering van hierdie aansigte.
Книги з теми "Grothendieck fibration"
Johnson, Niles, and Donald Yau. 2-Dimensional Categories. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198871378.001.0001.
Повний текст джерелаЧастини книг з теми "Grothendieck fibration"
Johnson, Niles, and Donald Yau. "Grothendieck Fibrations." In 2-Dimensional Categories, 331–70. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198871378.003.0009.
Повний текст джерела