Theorems · Definition · category theory
CategoryTheory.Limits.IsInitial
{C : Type u₁} → [CategoryTheory.Category.{v₁, u₁} C] → C → Type (max (max 0 u₁) v₁)X is initial if the cocone it induces on the empty diagram is colimiting.
- Cited by
- 158 results in Mathlib
- Foundations
- Depth 24 from the axioms, rests on 131 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.Limits.IsColimitproof · cited by 773
- CategoryTheory.Limits.asEmptyCoconeproof · cited by 6
Cited by279
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.IsInitial.tostatement and proof · cited by 119
- CategoryTheory.Limits.initialIsInitialstatement · cited by 35
- CategoryTheory.Limits.IsInitial.hom_extstatement and proof · cited by 32
- CategoryTheory.WithInitial.starInitialstatement · cited by 23
- CategoryTheory.Limits.IsInitial.ofIsostatement and proof · cited by 15
- CategoryTheory.StructuredArrow.IsUniversalproof · cited by 13
- CategoryTheory.zeroMulstatement and proof · cited by 12
- CategoryTheory.Limits.IsInitial.uniqueUpToIsostatement and proof · cited by 8
- CategoryTheory.Limits.IsInitial.hasInitialstatement and proof · cited by 7
- CategoryTheory.Under.equivalenceOfIsInitialstatement and proof · cited by 7
- CategoryTheory.WithInitial.liftToInitialstatement and proof · cited by 6
- CategoryTheory.Functor.PushoutObjObj.ofIsInitialLeftstatement and proof · cited by 6
Showing the 200 most cited of 279.