Model category
= Model category
{title2=$(\mathcal W,\mathcal F,\mathcal C)$}
{wiki}
A complete and cocomplete <category> with designated <model weak equivalences>, <model fibrations> and <model cofibrations>, closed under retracts. Weak equivalences satisfy two-out-of-three; maps admit the two cofibration/fibration factorizations, and either acyclic class has the required lifting property against the opposite class. These axioms organize homotopy-theoretic calculations abstractly.