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Theorems · Theorem · category theory

CategoryTheory.Sieve.functor_galoisConnection

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (F : CategoryTheory.Functor C D) (X : C),
  GaloisConnection (CategoryTheory.Sieve.functorPushforward F) (CategoryTheory.Sieve.functorPullback F)
Defined in
Mathlib.CategoryTheory.Sites.Sieves
Cited by
7 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Category

Around this declaration

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

CategoryTheory.Sieve.functorPushforward_le_iff_le_functorPullback · cited by 3Sieve.functorPushforward_…CategoryTheory.Sieve.fullyFaithfulFunctorGaloisCoinsertion · cited by 3Sieve.fullyFaithfulFuncto…CategoryTheory.Sieve.le_functorPushforward_pullback · cited by 2Sieve.le_functorPushforwa…CategoryTheory.Sieve.functorPullback_monotone · cited by 2Sieve.functorPullback_mon…CategoryTheory.Sieve.functorPullback_pushforward_le · cited by 2Sieve.functorPullback_pus…CategoryTheory.Sieve.functorPushforward_monotone · cited by 2Sieve.functorPushforward_…CategoryTheory.Sieve.functorPushforward_union · cited by 0Sieve.functorPushforward_…CategoryTheory.Sieve.functorPushforward_bot · cited by 0Sieve.functorPushforward_…CategoryTheory.Sieve.essSurjFullFunctorGaloisInsertion · cited by 0Sieve.essSurjFullFunctorG…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Category.id_comp · cited by 1998Category.id_compCategoryTheory.Sieve · cited by 552CategoryTheory.SieveCategoryTheory.Sieve.arrows · cited by 446Sieve.arrowsGaloisConnection · cited by 253GaloisConnectionCategoryTheory.Sieve.functorPushforward · cited by 73Sieve.functorPushforwardCategoryTheory.Sieve.functorPullback · cited by 49Sieve.functorPullbackCategoryTheory.Sieve.downward_closed · cited by 39Sieve.downward_closedSieve.functor_galoisConnectionCITED BYCITES

Cites14

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Cited by9

Results whose statement or proof uses this declaration.