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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.Sievestatement and proof · cited by 552
- CategoryTheory.Sieve.arrowsproof · cited by 446
- GaloisConnectionstatement · cited by 253
- CategoryTheory.Sieve.functorPushforwardstatement and proof · cited by 73
Cited by9
Results whose statement or proof uses this declaration.
- CategoryTheory.Sieve.functorPushforward_le_iff_le_functorPullbackproof · cited by 3
- CategoryTheory.Sieve.fullyFaithfulFunctorGaloisCoinsertionproof · cited by 3
- CategoryTheory.Sieve.le_functorPushforward_pullbackproof · cited by 2
- CategoryTheory.Sieve.functorPullback_monotoneproof · cited by 2
- CategoryTheory.Sieve.functorPullback_pushforward_leproof · cited by 2
- CategoryTheory.Sieve.functorPushforward_monotoneproof · cited by 2
- CategoryTheory.Sieve.functorPushforward_unionproof · cited by 0
- CategoryTheory.Sieve.functorPushforward_botproof · cited by 0
- CategoryTheory.Sieve.essSurjFullFunctorGaloisInsertionproof · cited by 0