Theorems · Inductive type · category theory

CategoryTheory.ExponentialIdeal

{C : Type u₁} →
  {D : Type u₂} →
    [inst : CategoryTheory.Category.{v₁, u₁} C] →
      [inst_1 : CategoryTheory.Category.{v₁, u₂} D] →
        CategoryTheory.Functor D C →
          [inst_2 : CategoryTheory.CartesianMonoidalCategory C] → [CategoryTheory.MonoidalClosed C] → Prop

The subcategory D of C expressed as an inclusion functor is an exponential ideal if B ∈ D implies A ⟹ B ∈ D for all A.

Defined in

Mathlib.CategoryTheory.Monoidal.Closed.Ideal

Cited by

8 results in Mathlib

Foundations

Depth 3 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.MonoidalClosed