Basic properties of left homotopy: 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.

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.

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

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

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

Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.

Explores natural transformations in algebra, defining functors and isomorphisms.

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