Theorems · Inductive type · category theory

CategoryTheory.Dial

(C : Type u) → [inst : CategoryTheory.Category.{v, u} C] → [CategoryTheory.Limits.HasFiniteProducts C] → Type (max u v)

The Dialectica category. An object of the category is a triple ⟨U, X, α ⊆ U × X⟩, and a morphism from ⟨U, X, α⟩ to ⟨V, Y, β⟩ is a pair (f : U ⟶ V, F : U ⨯ Y ⟶ X) such that {(u,y) | α(u, F(u, y))} ⊆ {(u,y) | β(f(u), y)}. The subset α is actually encoded as an element of Subobject (U × X), and the above inequality is expressed using pullbacks.

Defined in

Mathlib.CategoryTheory.Dialectica.Basic

Cited by

80 results in Mathlib

Foundations

Depth 2 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasFiniteProducts