Theorems · Definition · category theory
CategoryTheory.Subfunctor.IsFinite.recOn
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{F : CategoryTheory.Functor Cᵒᵖ (Type w)} →
{G : CategoryTheory.Subfunctor F} →
{motive : G.IsFinite → Sort u_1} →
(t : G.IsFinite) →
((exists_isGeneratedBy : ∃ ι, ∃ (_ : Finite ι), ∃ X x, Nonempty (G.IsGeneratedBy x)) → motive ⋯) → motive t- Defined in
- Mathlib.CategoryTheory.Subfunctor.Finite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- Finitestatement and proof · cited by 3,029
- CategoryTheory.Subfunctorstatement and proof · cited by 112
- CategoryTheory.Subfunctor.IsGeneratedBystatement and proof · cited by 11
- CategoryTheory.Subfunctor.IsFinitestatement and proof · cited by 5
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