Theorems · Inductive type · category theory
CategoryTheory.Limits.HasFiniteLimits
(C : Type u) → [CategoryTheory.Category.{v, u} C] → PropA category has all finite limits if every functor J ⥤ C with a FinCategory J
instance and J : Type has a limit.
This is often called 'finitely complete'.
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
Cited by50
Results whose statement or proof uses this declaration.
- CategoryTheory.flat_of_preservesFiniteLimitsstatement and proof · cited by 4
- CategoryTheory.StructuredArrow.projectSubobjectstatement and proof · cited by 4
- CategoryTheory.hasInitial_of_isCoseparatingproof · cited by 2
- CategoryTheory.Limits.hasFiniteLimits_of_hasEqualizers_and_finite_productsstatement · cited by 2
- CategoryTheory.IsCofiltered.of_hasFiniteLimitsstatement and proof · cited by 2
- CategoryTheory.hasExactColimitsOfShape_discrete_of_hasExactColimitsOfShape_finset_discretestatement and proof · cited by 2
- CategoryTheory.hasExactColimitsOfShape_of_finalstatement and proof · cited by 2
- CategoryTheory.CountableAB4.of_hasExactColimitsOfShape_nat_and_finitestatement and proof · cited by 1
- CommRingCat.Under.hasFiniteLimitsstatement · cited by 1
- CategoryTheory.HasExactColimitsOfShape.domain_of_functorstatement and proof · cited by 1
- CategoryTheory.Limits.hasFiniteLimits_of_hasLimitsOfSizestatement · cited by 1