Theorems · Definition · category theory

CategoryTheory.AB5OfSize.recOn

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasFilteredColimitsOfSize.{w, w', v, u} C] →
      {motive : CategoryTheory.AB5OfSize.{w, w', v, u} C → Sort u_1} →
        (t : CategoryTheory.AB5OfSize.{w, w', v, u} C) →
          ((ofShape :
                ∀ (J : Type w') [inst_2 : CategoryTheory.Category.{w, w'} J] [inst_3 : CategoryTheory.IsFiltered J],
                  CategoryTheory.HasExactColimitsOfShape J C) →
              motive ⋯) →
            motive t

Defined in

Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic

Cited by

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Foundations

Depth 6 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasFilteredColimitsOfSize