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Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.toPrecoverage

{C : Type u_2} →
  [inst : CategoryTheory.Category.{u_3, u_2} C] → CategoryTheory.GrothendieckTopology C → CategoryTheory.Precoverage C

The induced coverage by a Grothendieck topology as a precoverage.

Defined in
Mathlib.CategoryTheory.Sites.PrecoverageToGrothendieck
Cited by
12 results in Mathlib
Foundations
Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Functor.restrictedTopology · cited by 14Functor.restrictedTopologyCategoryTheory.Precoverage.galoisConnection_toGrothendieck_toPrecoverage · cited by 6Precoverage.galoisConnect…CategoryTheory.Precoverage.toGrothendieck_le_iff_le_toPrecoverage · cited by 4Precoverage.toGrothendiec…CategoryTheory.Functor.coverPreserving_restrictedTopology · cited by 3Functor.coverPreserving_r…CategoryTheory.GrothendieckTopology.mem_toPrecoverage_iff · cited by 3GrothendieckTopology.mem_…CategoryTheory.Precoverage.Generates.le_toPrecoverage · cited by 3Generates.le_toPrecoverageCategoryTheory.Precoverage.toGrothendieck_comap_le_restrictedTopology · cited by 2Precoverage.toGrothendiec…CategoryTheory.GrothendieckTopology.OneHypercover.toZeroHypercover · cited by 1OneHypercover.toZeroHyper…CategoryTheory.Precoverage.le_toPrecoverage_toGrothendieck · cited by 1Precoverage.le_toPrecover…CategoryTheory.GrothendieckTopology.OneHypercover.toZeroHypercover_toPreZeroHypercover · cited by 0OneHypercover.toZeroHyper…CategoryTheory.GrothendieckTopology.arrows_mem_toPrecoverage_iff · cited by 0GrothendieckTopology.arro…CategoryTheory.Precoverage.Generates.casesOn · cited by 0Generates.casesOnCategoryTheory.GrothendieckTopology.toGrothendieck_toPrecoverage_le · cited by 0GrothendieckTopology.toGr…CategoryTheory.Precoverage.Generates.recOn · cited by 0Generates.recOnCategoryTheory.GrothendieckTopology.toPrecoverage_monotone · cited by 0GrothendieckTopology.toPr…DFunLike.coe · cited by 62936DFunLike.coeCategoryTheory.Category · cited by 32673CategoryTheory.CategorySet.ofPred · cited by 6101Set.ofPredCategoryTheory.GrothendieckTopology · cited by 1415CategoryTheory.Grothendie…CategoryTheory.Presieve · cited by 449CategoryTheory.PresieveCategoryTheory.Precoverage · cited by 204CategoryTheory.PrecoverageCategoryTheory.Sieve.generate · cited by 117Sieve.generateGrothendieckTopology.toPrecov…CITED BYCITES

Cites7

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Cited by16

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