Theorems · Definition · category theory
CategoryTheory.Mat_.embedding
(C : Type u₁) →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
[inst_1 : CategoryTheory.Preadditive C] → CategoryTheory.Functor C (CategoryTheory.Mat_ C)The embedding of C into Mat_ C as one-by-one matrices.
(We index the summands by PUnit.)
- Defined in
- Mathlib.CategoryTheory.Preadditive.Mat
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.Mat_statement · cited by 44
- CategoryTheory.Mat_.ιproof · cited by 29
Cited by24
Results whose statement or proof uses this declaration.
- CategoryTheory.Mat_.additiveObjIsoBiproductstatement and proof · cited by 8
- CategoryTheory.Mat_.isoBiproductEmbeddingstatement and proof · cited by 6
- CategoryTheory.Mat_.additiveObjIsoBiproduct_hom_πstatement and proof · cited by 2
- CategoryTheory.Mat_.additiveObjIsoBiproduct_naturalitystatement and proof · cited by 2
- CategoryTheory.Mat_.embeddingLiftIsostatement and proof · cited by 2
- CategoryTheory.Mat_.equivalenceSelfOfHasFiniteBiproductsproof · cited by 2
- CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality'statement and proof · cited by 1
- CategoryTheory.Mat_.embedding_mapstatement and proof · cited by 1
- CategoryTheory.Mat_.isoBiproductEmbedding_homstatement · cited by 1
- CategoryTheory.Mat_.isoBiproductEmbedding_invstatement · cited by 1
- CategoryTheory.Mat_.ι_additiveObjIsoBiproduct_invstatement and proof · cited by 1
- CategoryTheory.Mat_.ι_additiveObjIsoBiproduct_inv_assocstatement and proof · cited by 1