Theorems · Theorem · category theory
CategoryTheory.Prod.hom_ext_iff
∀ {C : Type u₁} [inst : CategoryTheory.CategoryStruct.{v₁, u₁} C] {D : Type u₂}
[inst_1 : CategoryTheory.CategoryStruct.{v₂, u₂} D] {X Y : C × D} {f g : X ⟶ Y}, f = g ↔ f.1 = g.1 ∧ f.2 = g.2- Defined in
- Mathlib.CategoryTheory.Products.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- CategoryTheory.CategoryStructstatement and proof · cited by 343
- CategoryTheory.Prod.hom_extproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.isIso_prod_iffproof · cited by 1
- CategoryTheory.Prod.mkHom_eqproof · cited by 0