Theorems · Theorem · category theory
CategoryTheory.Presieve.FamilyOfElements.isAmalgamation_map_localPreimage
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {R R' : CategoryTheory.Functor Cᵒᵖ (Type w)} (φ : R ⟶ R')
{X : Cᵒᵖ} (r' : R'.obj X), ((CategoryTheory.Presieve.FamilyOfElements.localPreimage φ r').map φ).IsAmalgamation r'- Cited by
- 0 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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Cites13
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.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- Opposite.unopstatement and proof · cited by 2,231
- TypeCat.Funstatement · cited by 1,307
- CategoryTheory.Sieve.arrowsstatement and proof · cited by 446
- CategoryTheory.Presieve.FamilyOfElements.IsAmalgamationstatement · cited by 53
- CategoryTheory.Presheaf.imageSievestatement and proof · cited by 30
- CategoryTheory.Presieve.FamilyOfElements.mapstatement · cited by 15
- CategoryTheory.Presheaf.app_localPreimageproof · cited by 4
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