Theorems · Inductive type · category theory

CategoryTheory.IsCofiltered.cofilteredClosure.below

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.IsCofilteredOrEmpty C] →
      {α : Type w} →
        {f : α → C} →
          {motive : (a : C) → CategoryTheory.IsCofiltered.cofilteredClosure f a → Prop} →
            {a : C} → CategoryTheory.IsCofiltered.cofilteredClosure f a → Prop

Defined in: Mathlib.CategoryTheory.Filtered.Small
Cited by: 1 results in Mathlib
Foundations: Depth 3 from the axioms · uses no axioms
Assumes: CategoryTheory.Category CategoryTheory.IsCofilteredOrEmpty

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Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement · cited by 32,673
CategoryTheory.IsCofilteredOrEmptystatement · cited by 55
CategoryTheory.IsCofiltered.cofilteredClosurestatement · cited by 2

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.IsCofiltered.cofilteredClosure.brecOnstatement and proof · cited by 0
CategoryTheory.IsCofiltered.cofilteredClosure.below.casesOnstatement and proof · cited by 0