An introduction to model categories with examples
Xiao-Wu Chen
TL;DR
This paper provides an informal overview of model categories, illustrating key concepts through detailed examples involving small categories, dg algebras, and small dg categories.
Contribution
It offers an accessible introduction to model categories with concrete examples, aiding understanding of their structure and applications.
Findings
Detailed explanations of three important examples of model categories
Clarification of core concepts through illustrative cases
Enhanced understanding of model categories in different mathematical contexts
Abstract
We give an informal introduction to model categories, and treat three important examples in some details: the category of small categories, the category of dg algebras, and the category of small dg categories.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Intracranial Aneurysms: Treatment and Complications