Theorems · Definition · group theory
AddMonoid.Coprod.swap
(M : Type u_1) → (N : Type u_2) → [inst : AddZeroClass M] → [inst_1 : AddZeroClass N] → AddMonoid.Coprod M N →+ AddMonoid.Coprod N M
Map AddMonoid.Coprod M N to AddMonoid.Coprod N M
by applying Sum.swap to each element of the underlying list.
See also AddEquiv.coprodComm for an AddEquiv version.
- Defined in
- Mathlib.GroupTheory.Coprod.Basic
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 49 from the axioms · uses propext, Quot.sound
- Assumes
- AddZeroClassAddZeroClass
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.
- AddMonoidHomstatement · cited by 3,230
- AddZeroClassstatement and proof · cited by 1,237
- AddMonoidHom.compproof · cited by 339
- AddMonoid.Coprodstatement · cited by 104
- AddMonoid.Coprod.mkproof · cited by 16
- FreeAddMonoid.mapproof · cited by 14
- AddMonoid.Coprod.cliftproof · cited by 5
Cited by26
Results whose statement or proof uses this declaration.
- AddMonoid.Coprod.lift_comp_swapstatement · cited by 3
- AddMonoid.Coprod.swap_injectivestatement · cited by 3
- AddMonoid.Coprod.swap_surjectivestatement · cited by 3
- AddMonoid.Coprod.lift_swapstatement · cited by 2
- AddEquiv.coprodCommproof · cited by 2
- AddMonoid.Coprod.swap_swapstatement · cited by 2
- AddMonoid.Coprod.swap_comp_mapstatement · cited by 1
- AddMonoid.Coprod.swap_comp_swapstatement · cited by 1
- AddMonoid.Coprod.swap_eq_zerostatement and proof · cited by 1
- AddMonoid.Coprod.lift_inr_inlstatement · cited by 0
- AddEquiv.coprodComm_applystatement · cited by 0
- AddEquiv.coprodComm_symm_applystatement · cited by 0