The monoidal category structure on R
-coalgebras #
In Mathlib.RingTheory.Coalgebra.TensorProduct
, given two R
-coalgebras M, N
, we define a
coalgebra instance on M ⊗[R] N
, as well as the tensor product of two CoalgHom
s as a
CoalgHom
, and the associator and left/right unitors for coalgebras as CoalgEquiv
s.
In this file, we declare a MonoidalCategory
instance on the category of coalgebras, with data
fields given by the definitions in Mathlib.RingTheory.Coalgebra.TensorProduct
, and Prop
fields proved by pulling back the MonoidalCategory
instance on the category of modules,
using Monoidal.induced
.
Equations
- One or more equations did not get rendered due to their size.
@[simp]
The data needed to induce a MonoidalCategory
structure via
CoalgebraCat.instMonoidalCategoryStruct
and the forgetful functor to modules.
Equations
- One or more equations did not get rendered due to their size.
Instances For
@[simp]
theorem
CoalgebraCat.MonoidalCategory.inducingFunctorData_μIso
(R : Type u)
[CommRing R]
(x✝ x✝¹ : CoalgebraCat R)
: