Cartesian closure of Type #
Show that Type u₁
is cartesian closed, and C ⥤ Type u₁
is cartesian closed for C
a small
category in Type u₁
.
Note this implies that the category of presheaves on a small category C
is cartesian closed.
instance
CategoryTheory.instIsLeftAdjointTypeTypesObjToQuiverToCategoryStructFunctorToQuiverToCategoryStructCategoryToPrefunctorBinaryProductFunctor
(X : Type v₁)
:
Equations
- One or more equations did not get rendered due to their size.
Equations
- One or more equations did not get rendered due to their size.
instance
CategoryTheory.instHasFiniteProductsFunctorTypeTypesCategory
{C : Type u₁}
[CategoryTheory.Category.{v₁, u₁} C]
:
Equations
- ⋯ = ⋯
instance
CategoryTheory.instCartesianClosedFunctorTypeTypesCategoryInstHasFiniteProductsFunctorTypeTypesCategory
{C : Type v₁}
[CategoryTheory.SmallCategory C]
:
Equations
- One or more equations did not get rendered due to their size.