Fubini's Rule for Pushouts

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

Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.

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

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

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

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

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

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

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

Explores Quillen equivalences, emphasizing the preservation of cofibrations and acyclic cofibrations.