Theorems · Theorem · category theory
Prefunctor.congr_hom
∀ {U : Type u_1} {V : Type u_2} [inst : Quiver U] [inst_1 : Quiver V] {F G : U ⥤q V} (e : F = G) {X Y : U} (f : X ⟶ Y),
Quiver.homOfEq (F.map f) ⋯ ⋯ = G.map fAn equality of prefunctors gives an equality on homs.
- Defined in
- Mathlib.Combinatorics.Quiver.Prefunctor
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- Prefunctor.objstatement · cited by 1,241
- Prefunctor.mapstatement and proof · cited by 952
- Quiverstatement and proof · cited by 405
- Prefunctorstatement and proof · cited by 116
- Quiver.homOfEqstatement · cited by 21
- Prefunctor.congr_objstatement · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Quiv.hom_map_inv_map_of_isoproof · cited by 1