Lectures related to Homotopy Invariance: Push Out Product

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

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

Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.

Explores chain homotopy, projective complexes, and homotopy equivalences in chain complexes.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Introduces the homotopy category of a model category with inverted weak equivalences and unique homotopy equivalences.

Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.

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

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

Explores the equivalence of left and right homotopy for morphisms between bifibrant objects.

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

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

Explores derived functors in model categories, focusing on identity and homotopy categories.

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

Introduces the concept of a universal covering construction with examples like Hawaiian rings.

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

Explores homotopy equivalence in chain complexes, emphasizing path object construction and left/right homotopy characterization.

Explores the uniqueness of CW approximation and Whitehead's theorem through the construction of maps inducing isomorphisms on homotopic groups.

Explores the basic properties of left homotopy in model categories, focusing on weak equivalences and morphism relationships.

Explores wedges in pointed spaces, group structures, and the Echman-Hilton argument.