Littérature scientifique sur le sujet « Grothendieck category »
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Articles de revues sur le sujet "Grothendieck category"
Gorbunov, V. G. « Generalized Grothendieck category ». Siberian Mathematical Journal 28, no 5 (1988) : 734–39. http://dx.doi.org/10.1007/bf00969313.
Texte intégralNăstăsescu, C., et B. Torrecillas. « Atomical Grothendieck categories ». International Journal of Mathematics and Mathematical Sciences 2003, no 71 (2003) : 4501–9. http://dx.doi.org/10.1155/s0161171203209418.
Texte intégralPuig, Lluis. « Ordinary Grothendieck Groups of a Frobenius P-Category ». Algebra Colloquium 18, no 01 (mars 2011) : 1–76. http://dx.doi.org/10.1142/s1005386711000022.
Texte intégralCoghetto, Roland. « Non-Trivial Universes and Sequences of Universes ». Formalized Mathematics 30, no 1 (1 avril 2022) : 53–66. http://dx.doi.org/10.2478/forma-2022-0005.
Texte intégralARA, DIMITRI, DENIS-CHARLES CISINSKI et IEKE MOERDIJK. « The dendroidal category is a test category ». Mathematical Proceedings of the Cambridge Philosophical Society 167, no 01 (26 avril 2018) : 107–21. http://dx.doi.org/10.1017/s030500411800021x.
Texte intégralBarot, M., D. Kussin et H. Lenzing. « The Grothendieck group of a cluster category ». Journal of Pure and Applied Algebra 212, no 1 (janvier 2008) : 33–46. http://dx.doi.org/10.1016/j.jpaa.2007.04.007.
Texte intégralBergh, Petter Andreas, et Marius Thaule. « The Grothendieck group of an -angulated category ». Journal of Pure and Applied Algebra 218, no 2 (février 2014) : 354–66. http://dx.doi.org/10.1016/j.jpaa.2013.06.007.
Texte intégralBozicevic, M. « Grothendieck group of an equivariant derived category ». International Mathematical Forum 2 (2007) : 3219–31. http://dx.doi.org/10.12988/imf.2007.07296.
Texte intégralESTRADA, SERGIO, JAMES GILLESPIE et SINEM ODABAŞI. « Pure exact structures and the pure derived category of a scheme ». Mathematical Proceedings of the Cambridge Philosophical Society 163, no 2 (23 novembre 2016) : 251–64. http://dx.doi.org/10.1017/s0305004116000980.
Texte intégralSavoji, Fatemeh, et Reza Sazeedeh. « Local cohomology in Grothendieck categories ». Journal of Algebra and Its Applications 19, no 11 (14 novembre 2019) : 2050222. http://dx.doi.org/10.1142/s0219498820502229.
Texte intégralThèses sur le sujet "Grothendieck category"
McBride, Aaron. « Grothendieck Group Decategorifications and Derived Abelian Categories ». Thesis, Université d'Ottawa / University of Ottawa, 2015. http://hdl.handle.net/10393/33000.
Texte intégralBittmann, Léa. « Quantum Grothendieck rings, cluster algebras and quantum affine category O ». Thesis, Sorbonne Paris Cité, 2019. http://www.theses.fr/2019USPCC024.
Texte intégralThe aim of this thesis is to construct and study some quantum Grothendieck ring structure for the category O of representations of the Borel subalgebra Uq(^b) of a quantum affine algebra Uq(^g). First of all, we focus on the construction of asymptotical standard modules, analogs in the context of the category O of the standard modules in the category of finite-dimensional Uq(^g)-modules. A construction of these modules is given in the case where the underlying simple Lie algebra g is sl2. Next, we define a new quantum torus, which extends the quantum torus containing the quantum Grothendieck ring of the category of finite-dimensional modules. In order todo this, we use notions linked to quantum cluster algebras. In the same spirit, we build a quantum cluster algebra structure on the quantum Grothendieck ring of a monoidal subcategory CZ of the category of finite-dimensional representations. With this quantum torus, we de_ne the quantum Grothendieck ring Kt(O+Z) of a subcategory O+Z of the category O as a quantum cluster algebra. Then, we prove that this quantum Grothendieck ring contains that of the category of finite-dimensional representation. This result is first shown directly in type A, and then in all simply-laced types using the quantum cluster algebra structure of Kt(CZ). Finally, we define (q,t)-characters for some remarkable infinite-dimensional simple representations in the category O+Z. This enables us to write t-deformed analogs of important relations in the classical Grothendieck ring of the category O, which are related to the corresponding quantum integrable systems
Perera, Simon. « Grothendieck rings of theories of modules ». Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/grothendieck-rings-of-theories-of-modules(897cbbd9-77b6-47fb-8cf8-d15c7432e61b).html.
Texte intégralCagne, Pierre. « Towards a homotopical algebra of dependent types ». Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC063/document.
Texte intégralThis 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.
Texte intégralENGLISH 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.
Murfet, Daniel Saul. « The mock homotopy category of projectives and Grothendieck duality ». Phd thesis, 2007. http://hdl.handle.net/1885/151476.
Texte intégralAhmadi, Amir. « Axiomatic approach to cellular algebras ». Thesis, 2020. http://hdl.handle.net/1866/23949.
Texte intégralCellular algebras were introduced by J.J. Graham and G.I. Lehrer in 1996. They are a class of finite-dimensional associative algebras defined in terms of a “cellular datum” satisfying some axioms. This cellular datum, when made explicit for a given associative algebra, allows for the explicit construction of all its simple modules, up to isomorphism, and of their projective covers. In this work, we define these cellular algebras by introducing each building block of the cellular datum in a fairly axiomatic fashion. Two other families of associative algebras are discussed, namely the quasi-hereditary algebras and those whose modules form a highest weight category. These families were introduced at about the same period. The relationships between these two, and between them and the cellular ones, are made explicit.
Livres sur le sujet "Grothendieck category"
A, Grothendieck, et Cartier P, dir. The Grothendieck festschrift : A collection of articles written in honor of the 60th birthday of Alexander Grothendieck. Boston : Birkhauser, 2006.
Trouver le texte intégralM, Katz Nicholas, Manin Yuri I, Illusie Luc, Laumon Gérard et Ribet Kenneth A, dir. The Grothendieck Festschrift Volume III : A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck. Boston, MA : Birkhäuser Boston, 2007.
Trouver le texte intégralservice), SpringerLink (Online, dir. Frobenius categories versus Brauer blocks : The Grothendieck group of the Frobenius category of a Brauer block. Basel, Switzerland : Birkhäuser, 2009.
Trouver le texte intégralRobson, J. C. (James Christopher), 1940-, dir. Hereditary noetherian prime rings and idealizers. Providence, R.I : American Mathematical Society, 2011.
Trouver le texte intégralConference on Hopf Algebras and Tensor Categories (2011 University of Almeria). Hopf algebras and tensor categories : International conference, July 4-8, 2011, University of Almería, Almería, Spain. Sous la direction de Andruskiewitsch Nicolás 1958-, Cuadra Juan 1975- et Torrecillas B. (Blas) 1958-. Providence, Rhode Island : American Mathematical Society, 2013.
Trouver le texte intégral(Editor), Pierre Cartier, Luc Illusie (Editor), Nicholas M. Katz (Editor), Gérard Laumon (Editor), Yuri I. Manin (Editor) et Kenneth A. Ribet (Editor), dir. The Grothendieck Festschrift Volume I : A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck (Modern Birkhäuser Classics). Birkhäuser Boston, 2006.
Trouver le texte intégral(Editor), Pierre Cartier, Luc Illusie (Editor), Nicholas M. Katz (Editor), Gérard Laumon (Editor), Yuri I. Manin (Editor) et Kenneth A. Ribet (Editor), dir. The Grothendieck Festschrift Volume II : A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck (Modern Birkhäuser Classics). Birkhäuser Boston, 2006.
Trouver le texte intégral(Editor), Pierre Cartier, Luc Illusie (Editor), Nicholas M. Katz (Editor), Gérard Laumon (Editor), Yuri I. Manin (Editor) et Kenneth A. Ribet (Editor), dir. The Grothendieck Festschrift Volume III : A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck (Modern Birkhäuser Classics). Birkhäuser Boston, 2006.
Trouver le texte intégralCaramello, Olivia. Quotients of a theory of presheaf type. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.003.0010.
Texte intégralJohnson, Niles, et Donald Yau. 2-Dimensional Categories. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198871378.001.0001.
Texte intégralChapitres de livres sur le sujet "Grothendieck category"
Johnson, Niles, et Donald Yau. « The Grothendieck Construction ». Dans 2-Dimensional Categories, 371–438. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198871378.003.0010.
Texte intégral« The Grothendieck groups of a Frobenius P-category ». Dans Frobenius Categories versus Brauer Blocks, 211–39. Basel : Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-9998-6_15.
Texte intégral« Category of representations and constructions of Grothendieck groups and rings ». Dans Representation Theory and Higher Algebraic K-Theory, 31–50. Chapman and Hall/CRC, 2016. http://dx.doi.org/10.1201/b13624-7.
Texte intégralMcLarty, Colin. « Saunders Mac Lane : From Principia Mathematica through Göttingen to the Working Theory of Structures ». Dans The Prehistory of Mathematical Structuralism, 215–38. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780190641221.003.0009.
Texte intégralPalmgren, Erik. « On universes in type theory ». Dans Twenty Five Years of Constructive Type Theory. Oxford University Press, 1998. http://dx.doi.org/10.1093/oso/9780198501275.003.0012.
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