Theorems · Theorem · category theory

CategoryTheory.Dial.Hom.le

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasFiniteProducts C]
  [inst_2 : CategoryTheory.Limits.HasPullbacks C] {X Y : CategoryTheory.Dial C} (self : X.Hom Y),
  (CategoryTheory.Subobject.pullback (CategoryTheory.Limits.prod.lift CategoryTheory.Limits.prod.fst self.F)).obj
      X.rel ≤
    (CategoryTheory.Subobject.pullback
          (CategoryTheory.Limits.prod.map self.f (CategoryTheory.CategoryStruct.id Y.tgt))).obj
      Y.rel

This says {(u, y) | α(u, F(u, y))} ⊆ {(u, y) | β(f(u), y)} using subobject pullbacks

Defined in

Mathlib.CategoryTheory.Dialectica.Basic

Cited by

1 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasFiniteProductsCategoryTheory.Limits.HasPullbacks