Theorems · Theorem · category theory
CategoryTheory.Arrow.finite_iff
∀ (C : Type u) [inst : CategoryTheory.SmallCategory C], Finite (CategoryTheory.Arrow C) ↔ Nonempty (CategoryTheory.FinCategory C)
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.SmallCategory
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categoryproof · cited by 32,673
- Quiver.Homproof · cited by 32,603
- Fintypeproof · cited by 7,736
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- Equiv.symmproof · cited by 3,681
- Finitestatement and proof · cited by 3,029
- CategoryTheory.Comma.leftproof · cited by 886
- CategoryTheory.Arrowstatement and proof · cited by 713
- CategoryTheory.SmallCategorystatement and proof · cited by 480
- CategoryTheory.Arrow.mkproof · cited by 421
- CategoryTheory.Arrow.homproof · cited by 335
- Fintype.ofFiniteproof · cited by 255
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.isCardinalFiltered_aleph0_iffproof · cited by 1