nLab factorization systems - contents

factorization system

• orthogonal, strict

• weak, algebraic weak

• enriched

• reflective, stable

factorization system over a subcategory

k-ary factorization system, ternary factorization system

• factorization system in a 2-category

• factorization system in an (∞,1)-category

• orthogonal

Examples

• (epi, mono),

• (n-epi, n-mono)/n-image

  Postnikov system

• (eso, fully faithful),

(eso+full, faithful), (bo, ff)

• (hyperconnected, localic)