Theorems · Definition · group theory
AddMonoidHom.mgraph
{G : Type u_1} → {H : Type u_2} → [inst : AddMonoid G] → [inst_1 : AddMonoid H] → (G →+ H) → AddSubmonoid (G × H)The graph of a monoid homomorphism as a submonoid.
See also AddMonoidHom.graph for the graph as a subgroup.
- Defined in
- Mathlib.Algebra.Group.Graph
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Set.ofPredproof · cited by 6,101
- AddMonoidHomstatement and proof · cited by 3,230
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement · cited by 1,178
Cited by10
Results whose statement or proof uses this declaration.
- AddMonoidHom.graphproof · cited by 11
- AddMonoidHom.mem_mgraphstatement · cited by 7
- AddMonoidHom.exists_mrange_eq_mgraphstatement · cited by 4
- LinearMap.exists_range_eq_graphproof · cited by 2
- AddMonoidHom.exists_addEquiv_mrange_eq_mgraphstatement and proof · cited by 2
- AddSubmonoid.exists_addEquiv_eq_mgraphstatement and proof · cited by 1
- AddSubmonoid.exists_eq_mgraphstatement and proof · cited by 1
- AddMonoidHom.coe_mgraphstatement and proof · cited by 0
- AddMonoidHom.graph_toAddSubmonoidstatement · cited by 0
- AddMonoidHom.mgraph_eq_mrange_prodstatement · cited by 0