ScalingStacks

Remark 7.2. There is an obvious generalization of this definition to small pointed $\infty$-categories equipped with a suitable subcategory of “cofibrations” (satisfying the usual axioms, e.g. that cofibrations are stable under cobase change). However, in the presence of factorization hypotheses, this does not yield added generality; e.g., see [13, 1.3], which under such assumptions describes the $K$-theory space in terms of the Dwyer-Kan localization ${\mathcal{C}}$ regarded as a category with weak equivalences.