Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.Cover.Arrow.casesOn

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X : C} →
      {J : CategoryTheory.GrothendieckTopology C} →
        {S : J.Cover X} →
          {motive : S.Arrow → Sort u_1} →
            (t : S.Arrow) →
              ((Y : C) → (f : Y ⟶ X) → (hf : (↑S).arrows f) → motive { Y := Y, f := f, hf := hf }) → motive t

Defined in

Mathlib.CategoryTheory.Sites.Grothendieck

Cited by

13 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category