Theorems · Definition · category theory

CategoryTheory.Pretopology.toGrothendieck

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasPullbacks C] →
      CategoryTheory.Pretopology C → CategoryTheory.GrothendieckTopology C

A pretopology K can be completed to a Grothendieck topology J by declaring a sieve to be J-covering if it contains a family in K. See also [MM92] Chapter III, Section 2, Equation (2).

Defined in

Mathlib.CategoryTheory.Sites.Pretopology

Cited by

18 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacks