Unifying left and right homotopy: The homotopy relation

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

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

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

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

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

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

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

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

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

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