Theorems · Theorem · category theory

CategoryTheory.Precoverage.mem_comap_iff

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u_1} [inst_1 : CategoryTheory.Category.{v_1, u_1} D]
  {F : CategoryTheory.Functor C D} {J : CategoryTheory.Precoverage D} {X : C} {R : CategoryTheory.Presieve X},
  R ∈ (CategoryTheory.Precoverage.comap F J).coverings X ↔ CategoryTheory.Presieve.map F R ∈ J.coverings (F.obj X)

Defined in

Mathlib.CategoryTheory.Sites.Precoverage

Cited by

3 results in Mathlib

Foundations

Depth 5 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category