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Theorems · Definition · category theory

CategoryTheory.Pretopology.gi

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

We have a Galois insertion from pretopologies to Grothendieck topologies.

Defined in
Mathlib.CategoryTheory.Sites.Pretopology
Cited by
2 results in Mathlib
Foundations
Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacks
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Around this declaration

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Opens.pretopology_toGrothendieck · cited by 0Opens.pretopology_toGroth…CategoryTheory.Pretopology.toGrothendieck_bot · cited by 0Pretopology.toGrothendiec…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.GrothendieckTopology · cited by 1415CategoryTheory.Grothendie…CategoryTheory.Limits.HasPullbacks · cited by 439Limits.HasPullbacksGaloisInsertion · cited by 35GaloisInsertionCategoryTheory.Pretopology · cited by 32CategoryTheory.PretopologyCategoryTheory.Pretopology.toGrothendieck · cited by 18Pretopology.toGrothendieckCategoryTheory.GrothendieckTopology.toPretopology · cited by 3GrothendieckTopology.toPr…Pretopology.giCITED BYCITES

Cites7

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Cited by2

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