Theorems · Inductive type · category theory
CategoryTheory.Limits.HasFiniteWidePullbacks
(C : Type u) → [CategoryTheory.Category.{v, u} C] → PropA category HasFiniteWidePullbacks if it has all limits of shape WidePullbackShape J for
finite J, i.e. if it has a wide pullback for every finite collection of morphisms with the same
codomain.
- Cited by
- 6 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 by8
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.isContinuous_comap_forgetstatement and proof · cited by 1
- CategoryTheory.MorphismProperty.toGrothendieck_comap_forget_eq_inducedTopologystatement and proof · cited by 1
- CategoryTheory.Limits.hasFiniteWidePullbacks_opposite_iffstatement and proof · cited by 0
- CategoryTheory.Limits.hasFiniteWidePushouts_opposite_iffstatement and proof · cited by 0
- CategoryTheory.Limits.HasFiniteWidePullbacks.casesOnstatement and proof · cited by 0
- CategoryTheory.Limits.HasFiniteWidePullbacks.outstatement and proof · cited by 0
- CategoryTheory.Limits.HasFiniteWidePullbacks.recOnstatement and proof · cited by 0
- CategoryTheory.Over.ConstructProducts.over_finiteProducts_of_finiteWidePullbacksstatement and proof · cited by 0