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Theorems · Definition · commutative algebra

CommRingCat.mkUnder

(R : CommRingCat) → (A : Type u) → [inst : CommRing A] → [Algebra (↑R) A] → CategoryTheory.Under R

Make an object of Under R from an R-algebra.

Defined in
Mathlib.Algebra.Category.Ring.Under.Basic
Cited by
24 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingAlgebra

Around this declaration

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

AlgHom.toUnder · cited by 10AlgHom.toUndercommAlgCatEquivUnder · cited by 9commAlgCatEquivUnderCommRingCat.tensorProd · cited by 7CommRingCat.tensorProdCommRingCat.tensorProdObjIsoPushoutObj · cited by 5CommRingCat.tensorProdObj…AlgEquiv.toUnder · cited by 3AlgEquiv.toUnderCommRingCat.mkUnder_ext · cited by 2CommRingCat.mkUnder_extCommRingCat.Under.equalizerFork' · cited by 1Under.equalizerFork'CommRingCat.preservesLimit_parallelPair_tensorProd_iff_tensorEqualizer_bijective · cited by 1CommRingCat.preservesLimi…CommRingCat.Under.equalizer_comp · cited by 1Under.equalizer_compCommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right · cited by 1CommRingCat.pushout_inl_t…CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right · cited by 1CommRingCat.pushout_inr_t…CommRingCat.Under.equalizerFork'IsLimit · cited by 0Under.equalizerFork'IsLim…CommRingCat.Under.equalizerFork'_ι · cited by 0Under.equalizerFork'_ιCommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right_assoc · cited by 0CommRingCat.pushout_inl_t…commAlgCatEquivUnder_counitIso · cited by 0commAlgCatEquivUnder_coun…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraAlgebra.algebraMap · cited by 4706Algebra.algebraMapCommRingCat · cited by 2333CommRingCatCommRingCat.carrier · cited by 1096CommRingCat.carrierCategoryTheory.Under · cited by 276CategoryTheory.UnderCommRingCat.ofHom · cited by 259CommRingCat.ofHomCategoryTheory.Under.mk · cited by 65Under.mkCommRingCat.mkUnderCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by35

Results whose statement or proof uses this declaration.