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Theorems · Theorem · group theory

AddMonoidHom.id_comp

∀ {M : Type u_4} {N : Type u_5} [inst : AddZero M] [inst_1 : AddZero N] (f : M →+ N), (AddMonoidHom.id N).comp f = f
Defined in
Mathlib.Algebra.Group.Hom.Defs
Cited by
6 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Quot.sound
Assumes
AddZeroAddZero
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FreeAbelianGroup.toFinsupp_comp_toFreeAbelianGroup · cited by 1FreeAbelianGroup.toFinsup…Algebra.IsEffective.of_isEffective_tensorProduct_of_faithfullyFlat · cited by 1IsEffective.of_isEffectiv…IsAddIndecomposable.image_baseOf_neg_comp_eq · cited by 1IsAddIndecomposable.image…AddEquiv.comp_right_injective · cited by 0AddEquiv.comp_right_injec…AddCommGroup.DirectLimit.lift_of' · cited by 0DirectLimit.lift_of'AddCommGroup.DirectLimit.map_id · cited by 0DirectLimit.map_idAddMonoidHom · cited by 3230AddMonoidHomAddMonoidHom.comp · cited by 339AddMonoidHom.compAddMonoidHom.ext · cited by 149AddMonoidHom.extAddMonoidHom.id · cited by 107AddMonoidHom.idAddZero · cited by 87AddZeroAddMonoidHom.id_compCITED BYCITES

Cites5

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Cited by6

Results whose statement or proof uses this declaration.