Theorems · Definition · category theory
commHopfAlgCatEquivCogrpCommAlgCat
(R : Type u) → [inst : CommRing R] → CommHopfAlgCat R ≌ (CategoryTheory.Grp (CommAlgCat R)ᵒᵖ)ᵒᵖ
Commutative Hopf algebras over a commutative ring R are the same thing as cogroup
R-algebras.
- Defined in
- Mathlib.Algebra.Category.CommHopfAlgCat
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- CommRingstatement and proof · cited by 17,173
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Functor.idproof · cited by 3,333
- Opposite.unopproof · cited by 2,231
- Quiver.Hom.unopproof · cited by 903
- CategoryTheory.InducedCategory.Hom.homproof · cited by 850
- CategoryTheory.Equivalencestatement · cited by 601
- CategoryTheory.Mon.Hom.homproof · cited by 200
- CategoryTheory.Grpstatement and proof · cited by 144
Cited by8
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.hopfSpecproof · cited by 1
- AlgebraicGeometry.hopfSpec.fullyFaithfulproof · cited by 0
- commHopfAlgCatEquivCogrpCommAlgCat_counitIso_hom_appstatement and proof · cited by 0
- commHopfAlgCatEquivCogrpCommAlgCat_counitIso_inv_appstatement and proof · cited by 0
- commHopfAlgCatEquivCogrpCommAlgCat_functor_obj_unop_Xstatement and proof · cited by 0
- commHopfAlgCatEquivCogrpCommAlgCat_inverse_objstatement and proof · cited by 0
- commHopfAlgCatEquivCogrpCommAlgCat_unitIso_hom_appstatement and proof · cited by 0
- commHopfAlgCatEquivCogrpCommAlgCat_unitIso_inv_appstatement and proof · cited by 0