Theorems · Definition · group theory
Monoid.End.equiv
(M : Type u_9) → [inst : MulOne M] → Monoid.End M ≃ (M →* M)
The identity equivalence between the monoid of endomorphisms Monoid.End M and the type
M →* M of monoid homomorphisms from M to itself. Monoid.End M is definitionally (but not
reducibly) equal to M →* M.
- Defined in
- Mathlib.Algebra.Group.Equiv.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- MulOne
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivstatement · cited by 8,337
- MonoidHomstatement · cited by 3,629
- MulOnestatement and proof · cited by 65
- Monoid.Endstatement · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- Monoid.End.equiv_applystatement · cited by 0
- Monoid.End.equiv_symm_applystatement · cited by 0