Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.map_le_iff

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u_1} [inst_1 : CategoryTheory.Category.{v_1, u_1} D]
  (P : CategoryTheory.MorphismProperty C) {F : CategoryTheory.Functor C D} (Q : CategoryTheory.MorphismProperty D)
  [Q.RespectsIso], P.map F ≤ Q ↔ P ≤ Q.inverseImage F

Defined in

Mathlib.CategoryTheory.MorphismProperty.Basic

Cited by

3 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MorphismProperty.RespectsIso