Theorems · Theorem · category theory

CategoryTheory.Dial.Hom.mk.injEq

∀ {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} (f : X.src ⟶ Y.src)
  (F : X.src ⨯ Y.tgt ⟶ X.tgt)
  (le :
    (CategoryTheory.Subobject.pullback (CategoryTheory.Limits.prod.lift CategoryTheory.Limits.prod.fst F)).obj X.rel ≤
      (CategoryTheory.Subobject.pullback
            (CategoryTheory.Limits.prod.map f (CategoryTheory.CategoryStruct.id Y.tgt))).obj
        Y.rel)
  (f_1 : X.src ⟶ Y.src) (F_1 : X.src ⨯ Y.tgt ⟶ X.tgt)
  (le_1 :
    (CategoryTheory.Subobject.pullback (CategoryTheory.Limits.prod.lift CategoryTheory.Limits.prod.fst F_1)).obj X.rel ≤
      (CategoryTheory.Subobject.pullback
            (CategoryTheory.Limits.prod.map f_1 (CategoryTheory.CategoryStruct.id Y.tgt))).obj
        Y.rel),
  ({ f := f, F := F, le := le } = { f := f_1, F := F_1, le := le_1 }) = (f = f_1 ∧ F = F_1)

Defined in

Mathlib.CategoryTheory.Dialectica.Basic

Cited by

0 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasFiniteProductsCategoryTheory.Limits.HasPullbacks