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Sheaves of Algebras over Boolean Spaces

Posted By: AvaxGenius

Date: 16 May 2025 12:35:27

Sheaves of Algebras over Boolean Spaces comprehensively covers sheaf theory as applied to universal algebra. The text presents intuitive ideas from topology such as the notion of metric space and the concept of central idempotent from ring theory. These lead to the abstract notions of complex and factor element, respectively. Factor elements are defined by identities, discovered for shells for the first time, explaining why central elements in rings and lattices have their particular form. Categorical formulations of the many representations by sheaves begin with adjunctions and move to equivalences as the book progresses, generalizing Stone’s theorem for Boolean algebras.

Science Algebras Boolean Spaces Algebra Topology Category Theory Homological Algebra

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Almost Ring Theory

Posted By: AvaxGenius

Date: 14 Mar 2025 05:52:57

This book develops thorough and complete foundations for the method of almost etale extensions, which is at the basis of Faltings' approach to p-adic Hodge theory. The central notion is that of an "almost ring". Almost rings are the commutative unitary monoids in a tensor category obtained as a quotient V-Mod/S of the category V-Mod of modules over a fixed ring V; the subcategory S consists of all modules annihilated by a fixed ideal m of V, satisfying certain natural conditions.

Science Ring Theory Algebra Commutative Rings Algebras Algebraic Geometry Category Theory Homological Algebra Field Theory

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Rational Homotopy Theory and Differential Forms

Posted By: AvaxGenius

Date: 10 Feb 2025 05:51:31

This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham’s theorem on simplicial complexes. In addition, Sullivan’s results on computing the rational homotopy type from forms is presented.

Brouwer's theorem Homotopy Differential Forms Mathematics Science Algebraic Topology Category Theory Homological Algebra Commutative Rings Algebras Topology Algebra

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Riemannian Topology and Geometric Structures on Manifolds

Posted By: AvaxGenius

Date: 3 Feb 2025 15:59:34

Riemannian Topology and Geometric Structures on Manifolds results from a similarly entitled conference held at the University of New Mexico in Albuquerque. The various contributions to this volume discuss recent advances in the areas of positive sectional curvature, Kähler and Sasaki geometry, and their interrelation to mathematical physics, notably M and superstring theory. Focusing on these fundamental ideas, this collection presents articles with original results, and plausible problems of interest for future research.

Science Manifolds Topology Differential Geometry Geometry Category Theory Homological Algebra Algebraic Geometry

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Duality in 19th and 20th Century Mathematical Thinking

Posted By: AvaxGenius

Date: 3 Jul 2024 05:16:00

This volume brings together scholars across various domains of the history and philosophy of mathematics, investigating duality as a multi-faceted phenomenon. Encompassing both systematic analysis and historical examination, the book endeavors to elucidate the status, roles, and dynamics of duality within the realms of 19th and 20th-century mathematics. Eschewing a priori notions, the contributors embrace the diverse interpretations and manifestations of duality, thus presenting a nuanced and comprehensive perspective on this intricate subject.

Science Mathematical Thinking History of Mathematical Sciences Category Theory Homological Algebra General Algebraic Systems Mathematics

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Categorical Perspectives

Posted By: AvaxGenius

Date: 1 Feb 2024 05:56:35

Categorical Perspectives by Jürgen Koslowski, Austin Melton
English | PDF | 2001 | 285 Pages | ISBN : 0817641866 | 23.1 MB

"Categorical Perspectives" consists of introductory surveys as well as articles containing original research and complete proofs devoted mainly to the theoretical and foundational developments of category theory and its applications to other fields. A number of articles in the areas of topology, algebra and computer science reflect the varied interests of George Strecker to whom this work is dedicated. Notable also are an exposition of the contributions and importance of George Strecker's research and a survey chapter on general category theory. This work is an excellent reference text for researchers and graduate students in category theory and related areas.

Science Topology Category Theory Homological Algebra Algebra Manifolds Cell Complexes Mathematics

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Homotopical Topology, Second Edition

Posted By: AvaxGenius

Date: 15 Oct 2023 14:20:40

This textbook on algebraic topology updates a popular textbook from the golden era of the Moscow school of I. M. Gelfand. The first English translation, done many decades ago, remains very much in demand, although it has been long out-of-print and is difficult to obtain. Therefore, this updated English edition will be much welcomed by the mathematical community. Distinctive features of this book include: a concise but fully rigorous presentation, supplemented by a plethora of illustrations of a high technical and artistic caliber; a huge number of nontrivial examples and computations done in detail; a deeper and broader treatment of topics in comparison to most beginning books on algebraic topology; an extensive, and very concrete, treatment of the machinery of spectral sequences. The second edition contains an entirely new chapter on K-theory and the Riemann-Roch theorem (after Hirzebruch and Grothendieck).

Science Topology Homotopical Topology Category Theory Homological Algebra K-Theory Algebraic Topology

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Approximation Theorems in Commutative Algebra: Classical and Categorical Methods

Posted By: AvaxGenius

Date: 27 Jan 2023 17:40:07

Approximation Theorems in Commutative Algebra: Classical and Categorical Methods by J. Alajbegović , J. Močkoř
English | PDF | 1992 | 339 Pages | ISBN : 0792319486 | 43.3 MB

Various types of approximation theorems are frequently used in general commutative algebra, and they have been found to be useful tools in valuation theory, the theory of Abelian lattice ordered groups, multiplicative ideal theory, etc.
Part 1 of this volume is devoted to the investigation of approximation theorems from a classical point of view. The chapters of this part deal with fields and rings, partly ordered groups, and with multirings and d-groups.

Science Commutative Algebra Commutative Rings Algebras Category Theory Homological Algebra Order Lattices Ordered Algebraic Structures Mathematics Algebra Approximation Approximation Theorems

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Classically Semisimple Rings: A Perspective Through Modules and Categories

Posted By: AvaxGenius

Date: 21 Dec 2022 04:59:23

Classically Semisimple Rings is a textbook on rings, modules and categories, aimed at advanced undergraduate and beginning graduate students.

Science Mathematics Algebra Commutative Rings Algebras Category Theory Homological Algebra

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Groups, Rings, Lie and Hopf Algebras

Posted By: AvaxGenius

Date: 23 Nov 2022 15:54:40

Groups, Rings, Lie and Hopf Algebras by Yuri Bahturin
English | PDF | 2003 | 240 Pages | ISBN : 1402012209 | 21 MB

The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time.

Science Groups Rings Hopf Algebras Algebras , Lie Algebras Lie Algebras Algebra , Linear Algebra, Category Theory, Homological Algebra Linear Algebra Category Theory Homological Algebra Non-associative Rings

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Research in Computational Topology 2

Posted By: AvaxGenius

Date: 10 Sep 2022 08:00:31

This second volume of Research in Computational Topology is a celebration and promotion of research by women in applied and computational topology, containing the proceedings of the second workshop for Women in Computational Topology (WinCompTop) as well as papers solicited from the broader WinCompTop community. The multidisciplinary and international WinCompTop workshop provided an exciting and unique opportunity for women in diverse locations and research specializations to interact extensively and collectively contribute to new and active research directions in the field. The prestigious senior researchers that signed on to head projects at the workshop are global leaders in the discipline, and two of them were authors on some of the first papers in the field.

Science Topology Computational Topology Algebraic Topology Computer Science Statistics Category Theory Homological Algebra Manifolds Cell Complexes

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Sets, Logic and Categories

Posted By: AvaxGenius

Date: 10 Jul 2022 04:11:44

Sets, Logic and Categories by Peter J. Cameron
English | PDF | 1998 | 191 Pages | ISBN : 1852330562 | 14.8 MB

Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics that we do, through the Axiom of Choice, Gödel's Theorem, and the Skolem Paradox. But they are also rich mathematical theories in their own right, contributing techniques and results to working mathematicians such as the Compactness Theorem and module categories. The book is aimed at those who know some mathematics and want to know more about its building blocks. Set theory is first treated naively an axiomatic treatment is given after the basics of first-order logic have been introduced. The discussion is su pported by a wide range of exercises. The final chapter touches on philosophical issues. The book is supported by a World Wibe Web site containing a variety of supplementary material.

Science category theory compactness theorem model theory set theory Sets Logic Mathematics Mathematical Logic Foundations Category Theory Homological Algebra K-Theory

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Towards Higher Categories

Posted By: AvaxGenius

Date: 16 Apr 2022 21:27:02

Towards Higher Categories by John C. Baez
English | PDF | 2010 | 292 Pages | ISBN : 1441915230 | 4.1 MB

The purpose of this book is to give background for those who would like to delve into some higher category theory. It is not a primer on higher category theory itself. It begins with a paper by John Baez and Michael Shulman which explores informally, by analogy and direct connection, how cohomology and other tools of algebraic topology are seen through the eyes of n-category theory.

Science Algebraic topology Cohomology Category Theory Homological Algebra Algebraic Topology Topology Mathematics

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Cognitive Semantics of Artificial Intelligence: A New Perspective

Posted By: AvaxGenius

Date: 2 Feb 2021 23:20:41

This book addresses the issue of cognitive semantics’ aspects that cannot be represented by traditional digital and logical means. The problem of creating cognitive semantics can be resolved in an indirect way.

Cognitive Semantics Development Chaos Control Category Theory Mathematics Technology Programming Algorithms Patterns Engineering Relativistic Theory Quantum Fields ePub Science Electromagnetic Waves Cosmic String Artificial Intelligence Physics

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Category Theory in Context (Repost)

Posted By: arundhati

Date: 6 Sep 2020 09:49:17

Emily Riehl, "Category Theory in Context"
English | 9 Mar. 2017 | ASIN: B06XHZ82GF | 272 Pages | AZW3 | 11.19 MB

Science AZW3 Category Theory Mathematics

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