Theorems · Inductive type · category theory

CategoryTheory.TransfiniteCompositionOfShape

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (J : Type w) →
      [inst_1 : LinearOrder J] →
        [OrderBot J] → {X Y : C} → (X ⟶ Y) → [SuccOrder J] → [WellFoundedLT J] → Type (max (max u v) w)

Given a well-ordered type J, a morphism f : X ⟶ Y in a category C is a transfinite composition of shape J if we have a well order continuous functor F : J ⥤ C, an isomorphism F.obj ⊥ ≅ X, a colimit cocone for F whose point is Y, such that the composition X ⟶ F.obj ⊥ ⟶ Y is f.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Preorder.TransfiniteCompositionOfShape

Cited by

32 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext

Assumes

CategoryTheory.CategoryLinearOrderOrderBotSuccOrderWellFoundedLT