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MATH-436: Homotopical algebra

Summary

This course will provide an introduction to model category theory, which is an abstract framework for generalizing homotopy theory beyond topological spaces and continuous maps. We will study numerous examples of model categories and their applications in algebra and topology.

Lectures

Instructors

Official source

https://edu.epfl.ch/coursebook/en/homotopical-algebra-MATH-436

Moodle Page

http://go.epfl.ch/MATH-436

About this result

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Summary

Lectures

Instructors

Official source

https://edu.epfl.ch/coursebook/en/homotopical-algebra-MATH-436

Moodle Page

http://go.epfl.ch/MATH-436

About this result

Ontological neighbourhood

Mathematics

Algebra: Abstract algebra, Category theory

Topology: Algebraic topology, General topology

Mathematical logic: Set theory

Lectures in this course (54)

Functors and Adjunctions

Explores functors between categories and the conditions for left and right adjoints.

Categories and Functors

Covers categories, functors, and presheaf categories, exploring the relationships between objects and morphisms.

Limits and Colimits in Functor Categories

Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.

Limits and colimits in Top

Covers the concepts of limits and colimits in the category of Topological Spaces, emphasizing the relationship between colimit and limit constructions and adjunctions.

Simplicial Sets: Introduction and Products

Introduces simplicial sets and explores the construction of products with a geometric interpretation.

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