Stable orthogonal factorization systems

Content created by Fredrik Bakke and Egbert Rijke.

Created on 2023-05-09.
Last modified on 2024-03-12.

module orthogonal-factorization-systems.stable-orthogonal-factorization-systems where
open import foundation.universe-levels

open import orthogonal-factorization-systems.function-classes
open import orthogonal-factorization-systems.orthogonal-factorization-systems


A stable orthogonal factorization system, or stable factorization system for short, is an orthogonal factorization system whose left class is stable under pullbacks. The right class of an orthogonal factorization system, however, is always stable under pullbacks.


is-stable-orthogonal-factorization-system :
  {l1 lL lR : Level} 
  orthogonal-factorization-system l1 lL lR  UU (lsuc l1  lL)
is-stable-orthogonal-factorization-system OFS =
    ( left-class-orthogonal-factorization-system OFS)

See also

The equivalent notions of


Egbert Rijke, Michael Shulman, and Bas Spitters. Modalities in homotopy type theory. Logical Methods in Computer Science, 01 2020. URL:, arXiv:1706.07526, doi:10.23638/LMCS-16(1:2)2020.

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