Del 188 - Cambridge Studies in Advanced Mathematics

From Categories to Homotopy Theory

Inbunden, Engelska, 2020

AvBirgit Richter,Birgit (Universitat Hamburg) Richter

999 kr

Beställningsvara. Skickas inom 7-10 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology of small categories.

Produktinformation

Utgivningsdatum2020-04-16
Mått156 x 235 x 26 mm
Vikt680 g
FormatInbunden
SpråkEngelska
SerieCambridge Studies in Advanced Mathematics
Antal sidor400
FörlagCambridge University Press
ISBN9781108479622

Tillhör följande kategorier

Topologi inom Naturvetenskap och teknik

Introduction; Part I. Category Theory: 1. Basic notions in category theory; 2. Natural transformations and the Yoneda lemma; 3. Colimits and limits; 4. Kan extensions; 5. Comma categories and the Grothendieck construction; 6. Monads and comonads; 7. Abelian categories; 8. Symmetric monoidal categories; 9. Enriched categories; Part II. From Categories to Homotopy Theory: 10. Simplicial objects; 11. The nerve and the classifying space of a small category; 12. A brief introduction to operads; 13. Classifying spaces of symmetric monoidal categories; 14. Approaches to iterated loop spaces via diagram categories; 15. Functor homology; 16. Homology and cohomology of small categories; References; Index.

Mer från samma författare

Del 315

Structured Ring Spectra

Andrew Baker, Birgit Richter, Andrew (University of Glasgow) Baker, Birgit (Rheinische Friedrich-Wilhelms-Universitat Bonn) Richter

Häftad

1 179 kr

Mer från samma serie

Del 49

Enumerative Combinatorics: Volume 1

Richard P. Stanley, Richard P. (Massachusetts Institute of Technology) Stanley

Häftad

859 kr

Del 194

Elements of ∞-Category Theory

Emily Riehl, Dominic Verity, Maryland) Riehl, Emily (The Johns Hopkins University, Sydney) Verity, Dominic (Macquarie University

Inbunden

1 099 kr

Del 31

Representations and Cohomology: Volume 2, Cohomology of Groups and Modules

D. J. Benson, D. J. (University of Georgia) Benson, D. Benson, Bela Bollobas, W. Fulton

Häftad

939 kr

Del 74

Real Analysis and Probability

R. M. Dudley, R. M. (Massachusetts Institute of Technology) Dudley, Bela Bollobas, W. Fulton

Häftad

939 kr

Del 4

Ultrametric Calculus

W. H. Schikhof, Bela Bollobas

Häftad

1 159 kr

Del 15

Algebraic Homotopy

Hans Joachim Baues, Leipzig) Baues, Hans Joachim (Max-Planck-Institut fur Mathematik in den Naturwissenschaften

Häftad

1 499 kr

Del 64

Calculus of Variations

Jürgen Jost, Xianqing Li-Jost, Jürgen Jost, Leipzig) Jost, Jurgen (Max-Planck-Institut fur Mathematik in den Naturwissenschaften, Leipzig) Li-Jost, Xianqing (Max-Planck-Institut fur Mathematik in den Naturwissenschaften, Jurgen Jost, J. Rgen Jost

Häftad

1 149 kr