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Theorems · Theorem · group theory

DirectSum.coeAddMonoidHom_of

∀ {ι : Type v} {M : Type u_1} {S : Type u_2} [inst : DecidableEq ι] [inst_1 : AddCommMonoid M] [inst_2 : SetLike S M]
  [inst_3 : AddSubmonoidClass S M] (A : ι → S) (i : ι) (x : ↥(A i)),
  (DirectSum.coeAddMonoidHom A) ((DirectSum.of (fun i => ↥(A i)) i) x) = ↑x
Defined in
Mathlib.Algebra.DirectSum.Basic
Cited by
3 results in Mathlib
Foundations
Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqAddCommMonoidSetLikeAddSubmonoidClass
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Around this declaration

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

DirectSum.decompose_symm_of · cited by 7DirectSum.decompose_symm_…OrthogonalFamily.projection_directSum_coeAddHom · cited by 0OrthogonalFamily.projecti…DirectSum.coe_decomposeTensor_apply · cited by 0DirectSum.coe_decomposeTe…DFunLike.coe · cited by 62936DFunLike.coeAddCommMonoid · cited by 12281AddCommMonoidAddMonoidHom · cited by 3230AddMonoidHomSetLike · cited by 1084SetLikeDirectSum · cited by 446DirectSumAddSubmonoidClass · cited by 346AddSubmonoidClassDirectSum.of · cited by 122DirectSum.ofAddSubmonoidClass.subtype · cited by 12AddSubmonoidClass.subtypeDirectSum.toAddMonoid_of · cited by 8DirectSum.toAddMonoid_ofDirectSum.coeAddMonoidHom · cited by 8DirectSum.coeAddMonoidHomDirectSum.coeAddMonoidHom_ofCITED BYCITES

Cites10

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Cited by3

Results whose statement or proof uses this declaration.