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Theorems · Theorem · linear algebra

Submodule.comap_id

∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  (p : Submodule R M), Submodule.comap LinearMap.id p = p
Defined in
Mathlib.Algebra.Module.Submodule.Map
Cited by
5 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext
Assumes
SemiringAddCommMonoidModule
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Around this declaration

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

Submodule.le_comap_pow_of_le_comap · cited by 2Submodule.le_comap_pow_of…KaehlerDifferential.range_mapBaseChange · cited by 2KaehlerDifferential.range…Module.End.invtSubmodule.id · cited by 2invtSubmodule.idZLattice.comap_refl · cited by 0ZLattice.comap_reflLinearMap.index_comp · cited by 0LinearMap.index_compModule · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidSubmodule · cited by 7192SubmoduleLinearMap.id · cited by 625LinearMap.idSetLike.coe_injective · cited by 374SetLike.coe_injectiveSubmodule.comap · cited by 347Submodule.comapSubmodule.comap_idCITED BYCITES

Cites8

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Cited by5

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