Exact Categories and Categories of Sheaves PDF Download

Author: M. Barr
Publisher: Springer
ISBN: 3540369996
Category : Mathematics
Languages : en
Pages : 251

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Author: Masaki Kashiwara
Publisher: Springer Science & Business Media
ISBN: 3540279504
Category : Mathematics
Languages : en
Pages : 496

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Book Description
Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic manner starting from scratch and continuing with full proofs to the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization.

Author: Jack Kelly
Publisher: American Mathematical Society
ISBN: 1470470411
Category : Mathematics
Languages : en
Pages : 172

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Author: M. P. Fourman
Publisher: Springer
ISBN: 3540348492
Category : Mathematics
Languages : en
Pages : 798

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Author: Bradd T. Hart
Publisher: American Mathematical Soc.
ISBN: 0821883828
Category : Mathematics
Languages : en
Pages : 440

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Proceedings of a conference held at Centre de recherches mathematiques of the Universite de Montreal, June 18-20, 2009.

Author: Aurelio Carboni
Publisher: Springer
ISBN: 3540464352
Category : Mathematics
Languages : en
Pages : 497

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Book Description
With one exception, these papers are original and fully refereed research articles on various applications of Category Theory to Algebraic Topology, Logic and Computer Science. The exception is an outstanding and lengthy survey paper by Joyal/Street (80 pp) on a growing subject: it gives an account of classical Tannaka duality in such a way as to be accessible to the general mathematical reader, and to provide a key for entry to more recent developments and quantum groups. No expertise in either representation theory or category theory is assumed. Topics such as the Fourier cotransform, Tannaka duality for homogeneous spaces, braided tensor categories, Yang-Baxter operators, Knot invariants and quantum groups are introduced and studies. From the Contents: P.J. Freyd: Algebraically complete categories.- J.M.E. Hyland: First steps in synthetic domain theory.- G. Janelidze, W. Tholen: How algebraic is the change-of-base functor?.- A. Joyal, R. Street: An introduction to Tannaka duality and quantum groups.- A. Joyal, M. Tierney: Strong stacks andclassifying spaces.- A. Kock: Algebras for the partial map classifier monad.- F.W. Lawvere: Intrinsic co-Heyting boundaries and the Leibniz rule in certain toposes.- S.H. Schanuel: Negative sets have Euler characteristic and dimension.-

Author: P.I. Johnstone
Publisher: Springer
ISBN: 3540357629
Category : Mathematics
Languages : en
Pages : 271

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Author: B. Jacobs
Publisher: Gulf Professional Publishing
ISBN: 9780444508539
Category : Computers
Languages : en
Pages : 784

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This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.

Author: Chris Heunen
Publisher: Amsterdam University Press
ISBN: 9085550246
Category : Mathematics
Languages : en
Pages : 214

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Book Description
This dissertation studies the logic behind quantum physics, using category theory as the principal tool and conceptual guide. To do so, principles of quantum mechanics are modeled categorically. These categorical quantum models are justified by an embedding into the category of Hilbert spaces, the traditional formalism of quantum physics. In particular, complex numbers emerge without having been prescribed explicitly. Interpreting logic in such categories results in orthomodular property lattices, and furthermore provides a natural setting to consider quantifiers. Finally, topos theory, incorporating categorical logic in a refined way, lets one study a quantum system as if it were classical, in particular leading to a novel mathematical notion of quantum-

Author: Leonid Positselski
Publisher: Springer Nature
ISBN: 3031379055
Category : Mathematics
Languages : en
Pages : 225

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Semi-Infinite Geometry is a theory of "doubly infinite-dimensional" geometric or topological objects. In this book the author explains what should be meant by an algebraic variety of semi-infinite nature. Then he applies the framework of semiderived categories, suggested in his previous monograph titled Homological Algebra of Semimodules and Semicontramodules, (Birkhäuser, 2010), to the study of semi-infinite algebraic varieties. Quasi-coherent torsion sheaves and flat pro-quasi-coherent pro-sheaves on ind-schemes are discussed at length in this book, making it suitable for use as an introduction to the theory of quasi-coherent sheaves on ind-schemes. The main output of the homological theory developed in this monograph is the functor of semitensor product on the semiderived category of quasi-coherent torsion sheaves, endowing the semiderived category with the structure of a tensor triangulated category. The author offers two equivalent constructions of the semitensor product, as well as its particular case, the cotensor product, and shows that they enjoy good invariance properties. Several geometric examples are discussed in detail in the book, including the cotangent bundle to an infinite-dimensional projective space, the universal fibration of quadratic cones, and the important popular example of the loop group of an affine algebraic group.