Theorems · Definition · category theory

CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.Hom.fst

{A : Type u₁} →
  {B : Type u₂} →
    {C : Type u₃} →
      [inst : CategoryTheory.Category.{v₁, u₁} A] →
        [inst_1 : CategoryTheory.Category.{v₂, u₂} B] →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} C] →
            {F : CategoryTheory.Functor A B} →
              {G : CategoryTheory.Functor C B} →
                {X : Type u₄} →
                  [inst_3 : CategoryTheory.Category.{v₄, u₄} X] →
                    {x y : CategoryTheory.Limits.CategoricalPullback.CatCommSqOver F G X} →
                      CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.Hom X x y → (x.fst ⟶ y.fst)

the first component of f : Hom x y is a morphism x.fst ⟶ y.fst

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic

Cited by

47 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category