Model Category
Weak equivalences, cofibrations, and fibrations provide an abstract setting for homotopy theory. Riehl expresses the model axioms through two weak factorization systems; unpack their lifting and factorization requirements before using replacements.
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Category · Categorical Limit · categorical colimit · homotopy equivalence
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Start here: Categorical Homotopy Theory
Emily Riehl · Book · English · Free full text
§11.3 Model categories and Quillen functors, Definition 11.3.1, printed p. 138; §§11.1–11.2 Lifting problems and lifting properties / Weak factorization systems
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Category Theory in the library · Preparation and skip guidance