Theorems · Definition · category theory
CoalgCat.of
(R : Type u) → [inst : CommRing R] → (X : Type v) → [inst_1 : AddCommGroup X] → [inst_2 : Module R X] → [Coalgebra R X] → CoalgCat R
The object in the category of R-coalgebras associated to an R-coalgebra.
- Defined in
- Mathlib.Algebra.Category.CoalgCat.Basic
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- ModuleCatproof · cited by 1,429
- ModuleCat.ofproof · cited by 594
- Coalgebrastatement and proof · cited by 112
- CoalgCatstatement · cited by 63
Cited by26
Results whose statement or proof uses this declaration.
- CoalgEquiv.toCoalgIsostatement · cited by 8
- CoalgCat.ofHomstatement · cited by 7
- CoalgCat.of_comulstatement · cited by 0
- CoalgCat.of_counitstatement · cited by 0
- CoalgCat.rightUnitor_defstatement · cited by 0
- CoalgCat.tensorHom_defstatement · cited by 0
- CoalgEquiv.toCoalgIso_homstatement · cited by 0
- CoalgEquiv.toCoalgIso_invstatement · cited by 0
- CoalgEquiv.toCoalgIso_reflstatement · cited by 0
- CoalgEquiv.toCoalgIso_symmstatement · cited by 0
- CoalgEquiv.toCoalgIso_transstatement · cited by 0
- BialgCat.forget₂_coalgebra_objstatement · cited by 0