More Concise Algebraic Topology: Localization, Completion, and Model Categories

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Six model structures for DG-modules over DGAs: model category theory in homological action (2013, methodology): “Since every object is fibrant in all six of our model categories, we pass to homotopy categories by cofibrant approximation and passage to homotopy classes.”
∞-Categories for the Working Mathematician (2018, background): “The natural isomorphism on the 2To quote [41] “Thinking from the two points of view simultaneously, it is essential that the constructed ordinary category be isomorphic to the ordinary category that one started out with.”