Theorems · Inductive type · category theory

CategoryTheory.CoverPreserving

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        CategoryTheory.GrothendieckTopology C →
          CategoryTheory.GrothendieckTopology D → CategoryTheory.Functor C D → Prop

A functor G : (C, J) ⥤ (D, K) between sites is cover-preserving if for all covering sieves R in C, R.functorPushforward G is a covering sieve in D.

Defined in

Mathlib.CategoryTheory.Sites.CoverPreserving

Cited by

32 results in Mathlib

Foundations

Depth 2 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category