Reports of the Midwest Category Seminar I
Author | : J Benabou |
Publisher | : Springer |
Total Pages | : 189 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540355456 |
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Author | : J Benabou |
Publisher | : Springer |
Total Pages | : 189 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540355456 |
Author | : J. W. Gray |
Publisher | : Springer |
Total Pages | : 263 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540365486 |
Author | : S. MacLane |
Publisher | : Springer |
Total Pages | : 255 |
Release | : 2006-11-22 |
Genre | : Mathematics |
ISBN | : 3540361502 |
Author | : H. Applegate |
Publisher | : Springer |
Total Pages | : 147 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540362924 |
Author | : G.M. Kelly |
Publisher | : Springer |
Total Pages | : 386 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540372709 |
Author | : Colin McLarty |
Publisher | : Clarendon Press |
Total Pages | : 282 |
Release | : 1992-06-04 |
Genre | : |
ISBN | : 0191589497 |
The book covers elementary aspects of category theory and topos theory. It has few mathematical prerequisites, and uses categorical methods throughout rather than beginning with set theoretic foundations. It works with key notions such as cartesian closedness, adjunctions, regular categories, and the internal logic of a topos. Full statements and elementary proofs are given for the central theorems, including the fundamental theorem of toposes, the sheafification theorem, and the construction of Grothendieck toposes over any topos as base. Three chapters discuss applications of toposes in detail, namely to sets, to basic differential geometry, and to recursive analysis. - ;Introduction; PART I: CATEGORIES: Rudimentary structures in a category; Products, equalizers, and their duals; Groups; Sub-objects, pullbacks, and limits; Relations; Cartesian closed categories; Product operators and others; PART II: THE CATEGORY OF CATEGORIES: Functors and categories; Natural transformations; Adjunctions; Slice categories; Mathematical foundations; PART III: TOPOSES: Basics; The internal language; A soundness proof for topos logic; From the internal language to the topos; The fundamental theorem; External semantics; Natural number objects; Categories in a topos; Topologies; PART IV: SOME TOPOSES: Sets; Synthetic differential geometry; The effective topos; Relations in regular categories; Further reading; Bibliography; Index. -
Author | : J. L. Morris |
Publisher | : Springer |
Total Pages | : 283 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540361588 |
Author | : George M. Bergman |
Publisher | : American Mathematical Soc. |
Total Pages | : 400 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 0821804952 |
This book studies representable functors among well-known varieties of algebras. All such functors from associative rings over a fixed ring R to each of the categories of abelian groups, associative rings, Lie rings, and to several others are determined. Results are also obtained on representable functors on varieties of groups, semigroups, commutative rings, and Lie algebras. The book includes a "Symbol index", which serves as a glossary of symbols used and a list of the pages where the topics so symbolized are treated, and a "Word and phrase index". The authors have strived -- and succeeded -- in creating a volume that is very user-friendly.
Author | : Tobias Dyckerhoff |
Publisher | : Springer Nature |
Total Pages | : 230 |
Release | : 2019-10-17 |
Genre | : Mathematics |
ISBN | : 3030271242 |
This monograph initiates a theory of new categorical structures that generalize the simplicial Segal property to higher dimensions. The authors introduce the notion of a d-Segal space, which is a simplicial space satisfying locality conditions related to triangulations of d-dimensional cyclic polytopes. Focus here is on the 2-dimensional case. Many important constructions are shown to exhibit the 2-Segal property, including Waldhausen’s S-construction, Hecke-Waldhausen constructions, and configuration spaces of flags. The relevance of 2-Segal spaces in the study of Hall and Hecke algebras is discussed. Higher Segal Spaces marks the beginning of a program to systematically study d-Segal spaces in all dimensions d. The elementary formulation of 2-Segal spaces in the opening chapters is accessible to readers with a basic background in homotopy theory. A chapter on Bousfield localizations provides a transition to the general theory, formulated in terms of combinatorial model categories, that features in the main part of the book. Numerous examples throughout assist readers entering this exciting field to move toward active research; established researchers in the area will appreciate this work as a reference.