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Theorems · Theorem · category theory

CommRingCat.isFinitelyPresentable_under

∀ (R : CommRingCat) (S : CategoryTheory.Under R),
  (CommRingCat.Hom.hom S.hom).FinitePresentation → CategoryTheory.IsFinitelyPresentable S

If S is a finitely presented R-algebra, S : Under R is finitely presentable.

Defined in
Mathlib.Algebra.Category.Ring.FinitePresentation
Cited by
1 results in Mathlib
Foundations
Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

CommRingCat.isFinitelyPresentable_hom · cited by 0CommRingCat.isFinitelyPre…CommRingCat · cited by 2333CommRingCatCommRingCat.carrier · cited by 1096CommRingCat.carrierCommRingCat.Hom.hom · cited by 432Hom.homCategoryTheory.Under · cited by 276CategoryTheory.UnderCategoryTheory.Under.right · cited by 128Under.rightCategoryTheory.Under.hom · cited by 73Under.homRingHom.FinitePresentation · cited by 37RingHom.FinitePresentationCategoryTheory.IsFinitelyPresentable · cited by 16CategoryTheory.IsFinitely…CategoryTheory.isFinitelyPresentable_iff_preservesFilteredColimits · cited by 1CategoryTheory.isFinitely…CommRingCat.preservesFilteredColimits_coyoneda · cited by 1CommRingCat.preservesFilt…CommRingCat.isFinitelyPresent…CITED BYCITES

Cites10

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

Cited by1

Results whose statement or proof uses this declaration.