Theorems · Definition · category theory

CategoryTheory.Functor.relativelyRepresentable.fst

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {F : CategoryTheory.Functor C D} →
          {X Y : D} →
            {f : X ⟶ Y} → (hf : F.relativelyRepresentable f) → {a : C} → (g : F.obj a ⟶ Y) → F.obj (hf.pullback g) ⟶ X

Given a relatively representable morphism f : X ⟶ Y, then for any g : F.obj a ⟶ Y, hf.fst g denotes the first projection in the following diagram, given by the defining property of f being relatively representable `` hf.pullback g --F.map (hf.snd g)--> F.obj a | | hf.fst g g | | v v X -- f -> Y ``

Defined in

Mathlib.CategoryTheory.MorphismProperty.Representable

Cited by

16 results in Mathlib

Foundations

Depth 12 from the axioms · uses Classical.choice

Assumes

CategoryTheory.CategoryCategoryTheory.Category