Theorems · Definition · group theory
Monoid.Coprod.swap
(M : Type u_1) → (N : Type u_2) → [inst : MulOneClass M] → [inst_1 : MulOneClass N] → Monoid.Coprod M N →* Monoid.Coprod N M
Map M ∗ N to N ∗ M by applying Sum.swap to each element of the underlying list.
See also MulEquiv.coprodComm for a MulEquiv version.
- Defined in
- Mathlib.GroupTheory.Coprod.Basic
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 49 from the axioms · uses propext, Quot.sound
- Assumes
- MulOneClassMulOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MonoidHomstatement · cited by 3,629
- MulOneClassstatement and proof · cited by 1,018
- MonoidHom.compproof · cited by 469
- Monoid.Coprodstatement · cited by 109
- Monoid.Coprod.mkproof · cited by 16
- FreeMonoid.mapproof · cited by 13
- Monoid.Coprod.cliftproof · cited by 5
Cited by26
Results whose statement or proof uses this declaration.
- Monoid.Coprod.swap_injectivestatement · cited by 3
- Monoid.Coprod.swap_surjectivestatement · cited by 3
- Monoid.Coprod.lift_comp_swapstatement · cited by 3
- Monoid.Coprod.swap_swapstatement · cited by 2
- Monoid.Coprod.lift_swapstatement · cited by 2
- MulEquiv.coprodCommproof · cited by 2
- Monoid.Coprod.swap_comp_mapstatement · cited by 1
- Monoid.Coprod.swap_comp_swapstatement · cited by 1
- Monoid.Coprod.swap_eq_onestatement and proof · cited by 1
- Monoid.Coprod.range_swapstatement · cited by 0
- Monoid.Coprod.mrange_swapstatement and proof · cited by 0
- Monoid.Coprod.snd_comp_swapstatement · cited by 0