Corollary 6.1.28. Let \(\Aa \) be an abelian category. The triple \((\Ch (\Aa ), \textup {quasi-isos}, \textup {epis})\) is an \(\infty \)-category with weak equivalences and fibrations. It admits functorial factorizations, and is homotopy complete whenever \(\Aa \) satisfies (AB3\(^*\)) and (AB4\(^*\)), i.e. \(\Aa \) has small products and epimorphisms are closed under small products.
Proof. This is a special case of Proposition 6.1.27 applied to the abelian category \(\Aa \catop \), using that \(\Ch (\Aa \catop ) \simeq \Ch (\Aa )\catop \). □
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