Theorems · Definition · category theory
CategoryTheory.Sieve.galoisInsertionOfIsSplitEpi
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{X Y : C} →
(f : Y ⟶ X) →
[CategoryTheory.IsSplitEpi f] →
GaloisInsertion (CategoryTheory.Sieve.pushforward f) (CategoryTheory.Sieve.pullback f)If f is a split epi, the pushforward-pullback adjunction on sieves is reflective.
- Defined in
- Mathlib.CategoryTheory.Sites.Sieves
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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.Homstatement and proof · cited by 32,603
- CategoryTheory.Sievestatement · cited by 552
- CategoryTheory.Sieve.pullbackstatement · cited by 126
- CategoryTheory.IsSplitEpistatement and proof · cited by 46
- GaloisInsertionstatement · cited by 35
- CategoryTheory.Sieve.pushforwardstatement · cited by 13
- CategoryTheory.Sieve.galoisConnectionproof · cited by 8
- GaloisConnection.toGaloisInsertionproof · cited by 0
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