Theorems · Definition · combinatorics
SimpleGraph.induceHom
{V : Type u_1} →
{W : Type u_2} →
{G : SimpleGraph V} →
{G' : SimpleGraph W} →
{s : Set V} →
{t : Set W} → (φ : G →g G') → Set.MapsTo (⇑φ) s t → SimpleGraph.induce s G →g SimpleGraph.induce t G'The restriction of a morphism of graphs to induced subgraphs.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Maps
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Set.Elemstatement · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement · cited by 1,346
- Set.MapsTostatement and proof · cited by 732
- SimpleGraph.Homstatement and proof · cited by 139
- SimpleGraph.inducestatement · cited by 80
- Set.MapsTo.restrictproof · cited by 57
Cited by8
Results whose statement or proof uses this declaration.
- SimpleGraph.ComponentCompl.homproof · cited by 12
- SimpleGraph.induceHom_compstatement and proof · cited by 1
- SimpleGraph.induceHom_idstatement and proof · cited by 1
- SimpleGraph.induceHomOfLE_toHomstatement · cited by 0
- SimpleGraph.induceHom_injectivestatement · cited by 0
- SimpleGraph.ComponentCompl.hom_transproof · cited by 0
- SimpleGraph.coe_induceHomstatement · cited by 0
- SimpleGraph.induceHom.congr_simpstatement and proof · cited by 0