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Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.toPretopology

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

The largest pretopology generating the given Grothendieck topology. See [MM92] Chapter III, Section 2, Equations (3,4).

Defined in
Mathlib.CategoryTheory.Sites.Pretopology
Cited by
3 results in Mathlib
Foundations
Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacks
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CategoryTheory.Pretopology.gi · cited by 2Pretopology.giOpens.toPretopology_grothendieckTopology · cited by 1Opens.toPretopology_groth…CategoryTheory.GrothendieckTopology.mem_toPretopology · cited by 0GrothendieckTopology.mem_…CategoryTheory.Pretopology.sInf_ofGrothendieck · cited by 0Pretopology.sInf_ofGrothe…DFunLike.coe · cited by 62936DFunLike.coeCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomSet.ofPred · cited by 6101Set.ofPredCategoryTheory.GrothendieckTopology · cited by 1415CategoryTheory.Grothendie…CategoryTheory.Presieve · cited by 449CategoryTheory.PresieveCategoryTheory.Limits.HasPullbacks · cited by 439Limits.HasPullbacksCategoryTheory.Sieve.generate · cited by 117Sieve.generateCategoryTheory.Pretopology · cited by 32CategoryTheory.PretopologyGrothendieckTopology.toPretop…CITED BYCITES

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Cited by4

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