Theorems · Definition · category theory
CategoryTheory.Limits.initialIsInitial
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
[inst_1 : CategoryTheory.Limits.HasInitial C] → CategoryTheory.Limits.IsInitial (⊥_ C)An initial object is initial.
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.Limits.Cocone.ptproof · cited by 1,354
- CategoryTheory.Limits.Coconeproof · cited by 746
- CategoryTheory.Limits.HasInitialstatement and proof · cited by 185
- CategoryTheory.Limits.IsInitialstatement · cited by 158
- CategoryTheory.Functor.emptyproof · cited by 103
- CategoryTheory.Limits.initialstatement · cited by 84
- CategoryTheory.Limits.initial.toproof · cited by 63
Cited by53
Results whose statement or proof uses this declaration.
- CategoryTheory.Bicategory.lanIsKanproof · cited by 6
- colimitCoconeOfInitialAndPushoutsproof · cited by 6
- CategoryTheory.Bicategory.lanLiftIsKanproof · cited by 6
- CategoryTheory.Limits.initialIsoIsInitialproof · cited by 4
- CategoryTheory.Limits.HasZeroObject.zeroIsoInitialproof · cited by 4
- CategoryTheory.Limits.mulInitialproof · cited by 2
- CategoryTheory.WithInitial.starIsoInitialproof · cited by 2
- CategoryTheory.Subobject.botCoeIsoZeroproof · cited by 2
- CategoryTheory.Limits.initialMulproof · cited by 2
- CategoryTheory.isPullback_of_cofan_isVanKampenproof · cited by 2
- CategoryTheory.Limits.isColimitOfHasInitialOfPreservesColimitproof · cited by 2
- CategoryTheory.BinaryCofan.isPullback_initial_to_of_isVanKampenproof · cited by 1