Made-to-order Weak Factorization Systems
نویسنده
چکیده
Weak factorization systems Weak factorization systems are of paramount importance to homotopical algebra. This connection is best illustrated by the following definition, due to Joyal and Tierney [JT07]. Definition 1. A Quillen model structure on a category M, with a class of maps W called weak equivalences satisfying the 2-of-3 property, consists of two classes of maps C and F so that (C ∩W,F) and (C,F ∩W) are weak factorization systems. Definition 2. A weak factorization system (L,R) on a category M consists of two classes of maps so that • Any map f ∈M can be factored as f = r · ` with ` ∈ L and r ∈ R. • Any lifting problem, i.e., any commutative square (1) · L3` // · r∈R · // @@
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