Theorems · Inductive type · category theory

CategoryTheory.Functor.IsCocontinuous

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {D : Type u_2} →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        CategoryTheory.Functor C D →
          CategoryTheory.GrothendieckTopology C → CategoryTheory.GrothendieckTopology D → Prop

A functor G : (C, J) ⥤ (D, K) between sites is called cocontinuous (SGA 4 III 2.1) if for all covering sieves R in D, R.pullback G is a covering sieve in C.

Defined in

Mathlib.CategoryTheory.Sites.CoverLifting

Cited by

55 results in Mathlib

Foundations

Depth 2 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category