Left Homotopy as an Equivalence Relation: The Homotopy Relation in a Model Category

Related lectures (32)

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Explores the construction of cylinder objects in chain complexes over a field, focusing on left homotopy and interval chain complexes.

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

Explores Quillen pairs, equivalences, and derived functors in homotopical algebra.

Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.

Explores sets of left homotopy equivalence classes of morphisms in model categories.

Focuses on proving the construction of the homotopy category and its properties, including preservation of composition and uniqueness of functors.

Explores the Serre model structure, focusing on left and right homotopy equivalences.

Explores natural transformations in algebra, defining functors and isomorphisms.

Covers the Fundamental Theorem of homotopical algebra, Quillen pairs, and derived functors.

Covers the definition and properties of a model category, including fibrations, cofibrations, weak equivalences, and more.