Made-to-order Weak Factorization Systems

نویسنده

  • EMILY RIEHL
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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تاریخ انتشار 2013