Theorems · Definition · category theory
MulEquiv.toSingleObjEquiv
{M : Type u} →
{N : Type v} →
[inst : Monoid M] → [inst_1 : Monoid N] → M ≃* N → (CategoryTheory.SingleObj M ≌ CategoryTheory.SingleObj N)Reinterpret a monoid isomorphism f : M ≃* N as an equivalence SingleObj M ≌ SingleObj N.
- Defined in
- Mathlib.CategoryTheory.SingleObj
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- MulEquivstatement and proof · cited by 1,142
- CategoryTheory.Equivalencestatement · cited by 601
- MulEquiv.symmproof · cited by 482
- MulEquiv.toMonoidHomproof · cited by 126
- CategoryTheory.eqToIsoproof · cited by 97
- CategoryTheory.SingleObjstatement · cited by 88
- MonoidHom.toFunctorproof · cited by 6
Cited by8
Results whose statement or proof uses this declaration.
- MulEquiv.toSingleObjEquiv_counitIso_homstatement and proof · cited by 0
- MulEquiv.toSingleObjEquiv_counitIso_invstatement and proof · cited by 0
- MulEquiv.toSingleObjEquiv_functor_mapstatement and proof · cited by 0
- MulEquiv.toSingleObjEquiv_functor_objstatement and proof · cited by 0
- MulEquiv.toSingleObjEquiv_inverse_mapstatement and proof · cited by 0
- MulEquiv.toSingleObjEquiv_inverse_objstatement and proof · cited by 0
- MulEquiv.toSingleObjEquiv_unitIso_homstatement and proof · cited by 0
- MulEquiv.toSingleObjEquiv_unitIso_invstatement and proof · cited by 0