Theorems · Definition · category theory
CategoryTheory.Functor.mapMatId
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
[inst_1 : CategoryTheory.Preadditive C] →
(CategoryTheory.Functor.id C).mapMat_ ≅ CategoryTheory.Functor.id (CategoryTheory.Mat_ C)The identity functor induces the identity functor on matrix categories.
- Defined in
- Mathlib.CategoryTheory.Preadditive.Mat
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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.Homproof · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Isostatement · cited by 3,963
- CategoryTheory.Functor.idstatement · cited by 3,333
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.NatIso.ofComponentsproof · cited by 178
- CategoryTheory.eqToIsoproof · cited by 97
- CategoryTheory.Mat_statement and proof · cited by 44
- CategoryTheory.Functor.mapMat_statement · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.mapMatId_hom_appstatement and proof · cited by 0
- CategoryTheory.Functor.mapMatId_inv_appstatement and proof · cited by 0