Theorems · Definition · group theory
MonoidHom.graph
{G : Type u_1} → {H : Type u_2} → [inst : Group G] → [inst_1 : Group H] → (G →* H) → Subgroup (G × H)The graph of a group homomorphism as a subgroup.
See also MonoidHom.mgraph for the graph as a submonoid.
- Defined in
- Mathlib.Algebra.Group.Graph
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
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.
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement · cited by 3,593
- Submonoidproof · cited by 3,086
- MonoidHom.mgraphproof · cited by 8
Cited by10
Results whose statement or proof uses this declaration.
- MonoidHom.exists_mulEquiv_range_eq_graphstatement and proof · cited by 1
- Subgroup.goursat_surjectivestatement · cited by 1
- MonoidHom.graph_eq_range_prodstatement and proof · cited by 0
- MonoidHom.graph_toSubmonoidstatement and proof · cited by 0
- MonoidHom.coe_graphstatement and proof · cited by 0
- Subgroup.exists_eq_graphstatement · cited by 0
- Subgroup.goursatstatement and proof · cited by 0
- MonoidHom.exists_range_eq_graphstatement and proof · cited by 0
- MonoidHom.mem_graphstatement · cited by 0
- Subgroup.exists_mulEquiv_eq_graphstatement · cited by 0