Theorems · Theorem · category theory
commBialgCatEquivComonCommAlgCat_inverse_map_unop_hom
∀ {R : Type u} [inst : CommRing R] {A B : (CategoryTheory.Mon (CommAlgCat R)ᵒᵖ)ᵒᵖ} (f : A ⟶ B),
↑(CommBialgCat.Hom.hom ((commBialgCatEquivComonCommAlgCat R).inverse.map f)) = CommAlgCat.Hom.hom f.unop.hom.unop- Defined in
- Mathlib.Algebra.Category.CommBialgCat
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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Cites19
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.Functor.objstatement · cited by 19,642
- CommRingstatement and proof · cited by 17,173
- CategoryTheory.Functor.mapstatement · cited by 8,698
- Oppositestatement and proof · cited by 8,081
- AlgHomstatement · cited by 3,236
- Opposite.unopstatement · cited by 2,231
- CategoryTheory.Equivalence.inversestatement · cited by 1,130
- Quiver.Hom.unopstatement · cited by 903
- CategoryTheory.Monstatement and proof · cited by 465
- CategoryTheory.Mon.Xstatement · cited by 329
- CategoryTheory.Mon.Hom.homstatement · cited by 200
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