nLab algebraic model structures - table

Algebraic model structures: Quillen model structures, mainly on locally presentable categories, and their constituent categories with weak equivalences and weak factorization systems, that can be equipped with further algebraic structure and “freely generated” by small data.

structure	small-set-generated	small-category-generated	algebraicized
weak factorization system	combinatorial wfs	accessible wfs	algebraic wfs
model category	combinatorial model category	accessible model category	algebraic model category
construction method	small object argument	same as $\to$	algebraic small object argument