Theorems · Inductive type · category theory

CategoryTheory.Functor.IsDenseSubsite

{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.GrothendieckTopology C →
          CategoryTheory.GrothendieckTopology D → CategoryTheory.Functor C D → Prop

The functor G : C ⥤ D exhibits (C, J) as a dense subsite of (D, K) if G is cover-dense, locally fully-faithful, and S is a cover of C if and only if the image of S in D is a cover.

Defined in

Mathlib.CategoryTheory.Sites.DenseSubsite.Basic

Cited by

87 results in Mathlib

Foundations

Depth 2 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category