[PDF] Toposes Triples And Theories eBook

Author : P.T. Johnstone
Publisher : Courier Corporation
Page : 401 pages
File Size : 43,59 MB
Release : 2014-01-15
Category : Mathematics
ISBN : 0486493369

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Focusing on topos theory's integration of geometric and logical ideas into the foundations of mathematics and theoretical computer science, this volume explores internal category theory, topologies and sheaves, geometric morphisms, and other subjects. 1977 edition.

Author : Jacob Lurie
Publisher : Princeton University Press
Page : 944 pages
File Size : 17,61 MB
Release : 2009-07-26
Category : Mathematics
ISBN : 0691140480

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In 'Higher Topos Theory', Jacob Lurie presents the foundations of this theory using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language.

Author : John L. Bell
Publisher : Courier Corporation
Page : 290 pages
File Size : 20,10 MB
Release : 2008-01-01
Category : Mathematics
ISBN : 0486462862

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This text introduces topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topics include local set theories, fundamental properties of toposes, sheaves, local-valued sets, and natural and real numbers in local set theories. 1988 edition.

Author : Michael Barr
Publisher : American Mathematical Soc.
Page : 194 pages
File Size : 20,72 MB
Release : 2002
Category : Mathematics
ISBN : 0821828770

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Acyclic models is a method heavily used to analyze and compare various homology and cohomology theories appearing in topology and algebra. This book is the first attempt to put together in a concise form this important technique and to include all the necessary background. It presents a brief introduction to category theory and homological algebra. The author then gives the background of the theory of differential modules and chain complexes over an abelian category to state the main acyclic models theorem, generalizing and systemizing the earlier material. This is then applied to various cohomology theories in algebra and topology. The volume could be used as a text for a course that combines homological algebra and algebraic topology. Required background includes a standard course in abstract algebra and some knowledge of topology. The volume contains many exercises. It is also suitable as a reference work for researchers.

Author : Emily Riehl
Publisher : Courier Dover Publications
Page : 273 pages
File Size : 23,43 MB
Release : 2017-03-09
Category : Mathematics
ISBN : 0486820807

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Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.

Author : P. T. Johnstone
Publisher : Oxford University Press
Page : 836 pages
File Size : 18,67 MB
Release : 2002-09-12
Category : Computers
ISBN : 9780198515982

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Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas. Because of this, an account of topos theory which approaches the subject from one particular direction can only hope to give a partial picture; the aim of this compendium is to present as comprehensive an account as possible of all the main approaches and to thereby demonstrate the overall unity of the subject. The material is organized in such a way that readers interested in following a particular line of approach may do so by starting at an appropriate point in the text.

Author : Michael Barr
Publisher :
Page : 352 pages
File Size : 24,74 MB
Release : 1995
Category : Computers
ISBN :

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A wide coverage of topics in category theory and computer science is developed in this text, including introductory treatments of cartesian closed categories, sketches and elementary categorical model theory, and triples. Over 300 exercises are included.