This book develops abstract homotopy theory from the categorical
perspective with a particular focus on examples. Part I discusses
two competing perspectives by which one typically first encounters
homotopy (co)limits: either as derived functors definable when the
appropriate diagram categories admit a compatible model structure,
or through particular formulae that give the right notion in
certain examples. Emily Riehl unifies these seemingly rival
perspectives and demonstrates that model structures on diagram
categories are irrelevant. Homotopy (co)limits are explained to be
a special case of weighted (co)limits, a foundational topic in
enriched category theory. In Part II, Riehl further examines this
topic, separating categorical arguments from homotopical ones. Part
III treats the most ubiquitous axiomatic framework for homotopy
theory - Quillen's model categories. Here, Riehl simplifies
familiar model categorical lemmas and definitions by focusing on
weak factorization systems. Part IV introduces quasi-categories and
homotopy coherence.
General
Imprint: |
Cambridge UniversityPress
|
Country of origin: |
United Kingdom |
Series: |
New Mathematical Monographs |
Release date: |
May 2014 |
First published: |
May 2014 |
Authors: |
Emily Riehl
|
Dimensions: |
229 x 152 x 25mm (L x W x T) |
Format: |
Hardcover
|
Pages: |
372 |
ISBN-13: |
978-1-107-04845-4 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Topology >
Algebraic topology
|
LSN: |
1-107-04845-1 |
Barcode: |
9781107048454 |
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