Theorems · Theorem · category theory

CommRingCat.Under.equalizer_comp

∀ {R : CommRingCat} {A B : CategoryTheory.Under R} (f g : A ⟶ B),
  CategoryTheory.CategoryStruct.comp ((CommRingCat.toAlgHom f).equalizer (CommRingCat.toAlgHom g)).val.toUnder f =
    CategoryTheory.CategoryStruct.comp ((CommRingCat.toAlgHom f).equalizer (CommRingCat.toAlgHom g)).val.toUnder g

Defined in: Mathlib.Algebra.Category.Ring.Under.Limits
Cited by: 1 results in Mathlib
Foundations: Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites13

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

Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CommRingCatstatement and proof · cited by 2,333
Subalgebrastatement · cited by 1,353
CommRingCat.carrierstatement and proof · cited by 1,096
CategoryTheory.Understatement and proof · cited by 276
CategoryTheory.Under.rightstatement and proof · cited by 128
Subalgebra.valstatement · cited by 104
CommRingCat.mkUnderstatement · cited by 24
AlgHom.equalizerstatement and proof · cited by 21
CommRingCat.toAlgHomstatement and proof · cited by 13
AlgHom.toUnderstatement · cited by 10

Cited by2

Results whose statement or proof uses this declaration.

CommRingCat.Under.equalizerForkIsLimitproof · cited by 2
CommRingCat.preservesLimit_parallelPair_tensorProd_iff_tensorEqualizer_bijectiveproof · cited by 1