Theorems · Theorem · category theory
CategoryTheory.Functor.preimageIso_hom
∀ {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 Y : C} [inst_2 : F.Full] [inst_3 : F.Faithful] (f : F.obj X ≅ F.obj Y),
(F.preimageIso f).hom = F.preimage f.hom- Cited by
- 1 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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 · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Iso.homstatement and proof · cited by 7,684
- CategoryTheory.Isostatement and proof · cited by 3,963
- CategoryTheory.Functor.Fullstatement and proof · cited by 341
- CategoryTheory.Functor.Faithfulstatement and proof · cited by 313
- CategoryTheory.Functor.preimagestatement · cited by 55
- CategoryTheory.Functor.preimageIsostatement and proof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.preimageIso_mapIsoproof · cited by 0