Theorems · Theorem · category theory

CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.pullHom_id

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C]
  {F : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete Cᵒᵖ) CategoryTheory.Cat} ⦃X₁ X₂ : C⦄
  ⦃M₁ : ↑(F.obj { as := Opposite.op X₁ })⦄ ⦃M₂ : ↑(F.obj { as := Opposite.op X₂ })⦄ ⦃Y : C⦄ ⦃f₁ : Y ⟶ X₁⦄ ⦃f₂ : Y ⟶ X₂⦄
  (φ : (F.map f₁.op.toLoc).toFunctor.obj M₁ ⟶ (F.map f₂.op.toLoc).toFunctor.obj M₂),
  CategoryTheory.Pseudofunctor.LocallyDiscreteOpToCat.pullHom φ (CategoryTheory.CategoryStruct.id Y) f₁ f₂ ⋯ ⋯ = φ

Defined in

Mathlib.CategoryTheory.Sites.Descent.IsPrestack

Cited by

2 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category