Theorems · Theorem · group theory
AddMonoidHom.comp_apply
∀ {M : Type u_4} {N : Type u_5} {P : Type u_6} [inst : AddZero M] [inst_1 : AddZero N] [inst_2 : AddZero P] (g : N →+ P)
(f : M →+ N) (x : M), (g.comp f) x = g (f x)- Defined in
- Mathlib.Algebra.Group.Hom.Defs
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- AddMonoidHomstatement and proof · cited by 3,230
- AddMonoidHom.compstatement · cited by 339
- AddZerostatement and proof · cited by 87
Cited by12
Results whose statement or proof uses this declaration.
- AddSubmonoid.LocalizationMap.lift_of_compproof · cited by 2
- AddSubmonoid.LocalizationMap.lift_comp_liftproof · cited by 1
- AddCommGrpCat.Colimits.Quot.desc_toCocone_descproof · cited by 1
- AddSubmonoid.bsupr_eq_mrange_dfinsuppSumAddHomproof · cited by 1
- Finsupp.toFreeAbelianGroup_comp_toFinsuppproof · cited by 1
- AddCommGrpCat.Colimits.quotToQuotUlift_ιproof · cited by 1
- Finsupp.toFreeAbelianGroup_toFinsuppproof · cited by 1
- AddCommGrpCat.Colimits.quotUliftToQuot_ιproof · cited by 0
- AddMonoidHom.cancel_leftproof · cited by 0
- FreeAbelianGroup.toFinsupp_toFreeAbelianGroupproof · cited by 0
- AddGroupExtension.rightHom_comp_inlproof · cited by 0
- FreeAbelianGroup.lift_comp_applyproof · cited by 0