Theorems · Definition · category theory
CategoryTheory.Mat.equivalenceSingleObj
(R : Type) → [inst : Ring R] → CategoryTheory.Mat R ≌ CategoryTheory.Mat_ (CategoryTheory.SingleObj Rᵐᵒᵖ)
The categorical equivalence between the category of matrices over a ring, and the category of matrices over that ring considered as a single-object category.
- Defined in
- Mathlib.CategoryTheory.Preadditive.Mat
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
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Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- MulOppositestatement · cited by 1,135
- CategoryTheory.Equivalencestatement · cited by 601
- CategoryTheory.Equivalence.symmproof · cited by 195
- CategoryTheory.SingleObjstatement · cited by 88
- CategoryTheory.Functor.asEquivalenceproof · cited by 58
- CategoryTheory.Mat_statement · cited by 44
- CategoryTheory.Matstatement · cited by 11
- CategoryTheory.Mat.equivalenceSingleObjInverseproof · cited by 2
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