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Theorems · Definition · commutative algebra

ModuleCat.Derivation.d

{A B : CommRingCat} → {M : ModuleCat ↑B} → {f : A ⟶ B} → M.Derivation f → ↑B → ↑M

The underlying map B → M of a derivation M.Derivation f when M : ModuleCat B and f : A ⟶ B is a morphism in CommRingCat.

Defined in
Mathlib.Algebra.Category.ModuleCat.Differentials.Basic
Cited by
6 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Quot.sound
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Around this declaration

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

CommRingCat.KaehlerDifferential.d · cited by 5KaehlerDifferential.dPresheafOfModules.Derivation'.mk · cited by 1Derivation'.mkModuleCat.Derivation.d_add · cited by 0Derivation.d_addModuleCat.Derivation.d_map · cited by 0Derivation.d_mapModuleCat.Derivation.d_mul · cited by 0Derivation.d_mulModuleCat.Derivation.desc_d · cited by 0Derivation.desc_dPresheafOfModules.Derivation'.app_apply · cited by 0Derivation'.app_applyPresheafOfModules.Derivation'.mk_app · cited by 0Derivation'.mk_appDFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomCommRingCat · cited by 2333CommRingCatModuleCat · cited by 1429ModuleCatCommRingCat.carrier · cited by 1096CommRingCat.carrierModuleCat.carrier · cited by 997ModuleCat.carrierDerivation.toLinearMap · cited by 21Derivation.toLinearMapModuleCat.Derivation · cited by 5ModuleCat.DerivationDerivation.dCITED BYCITES

Cites8

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Cited by8

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