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Course# 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.

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Instructors (1)

Related concepts (78)

Homotopy

In topology, a branch of mathematics, two continuous functions from one topological space to another are called homotopic (from ὁμός "same, similar" and τόπος "place") if one can be "continuously d

Homological algebra

Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinato

Algebraic geometry

Algebraic geometry is a branch of mathematics which classically studies zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly fro

Model category

In mathematics, particularly in homotopy theory, a model category is a with distinguished classes of morphisms ('arrows') called 'weak equivalences', 'fibrations' and 'cofibrations' satisfying certa

Map

A map is a symbolic depiction emphasizing relationships between elements of some space, such as objects, regions, or themes.
Many maps are static, fixed to paper or some other durable medium, whil

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Lectures in this course (49)

Chapter 1(a): Categories, Functors, and Natural Transformations

Ep 1: Categories

Chapter 1(a): Categories, Functors, and Natural Transformations

Ep 3: Natural transformations

Chapter 1(b): Adjunctions

Ep 4: Theory, part 1