Theorems · Theorem · category theory

CategoryTheory.Dial.comp_le_lemma

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

Defined in

Mathlib.CategoryTheory.Dialectica.Basic

Cited by

0 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasFiniteProductsCategoryTheory.Limits.HasPullbacks