Homotopical Algebra: The Homotopy Category of a Model Category

Related lectures (32)

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Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.

Covers two technical lemmas essential for the Fundamental Theorem in homotopical algebra.

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

Covers the relationship between model categories and homotopy categories through functors preserving structural properties.

Explores the homotopy category of chain complexes and the relation between quasi-isomorphisms and chain homotopy equivalences.

Covers cylinders, path objects, and homotopy in model categories.

Introduces the course on homotopical algebra, exploring the power of analogy in pure mathematics.

Covers the transfer of model structures through adjunctions in the context of model categories.

Covers the properties and structures of model categories, focusing on factorizations, model structures, and homotopy of continuous maps.

Explores the left homotopy relation as an equivalence relation in model categories.