Theorems · Definition · category theory
CategoryTheory.Limits.IsInitial.to
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] → {X : C} → CategoryTheory.Limits.IsInitial X → (Y : C) → X ⟶ YGive the morphism from an initial object to any other.
- Cited by
- 119 results in Mathlib
- Foundations
- Depth 25 from the axioms, rests on 134 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Limits.IsInitialstatement and proof · cited by 158
- CategoryTheory.Limits.IsColimit.descproof · cited by 144
- CategoryTheory.Limits.asEmptyCoconeproof · cited by 6
Cited by172
Results whose statement or proof uses this declaration.
- CategoryTheory.WithInitial.mkCommaObjectproof · cited by 22
- CategoryTheory.WithInitial.opEquivproof · cited by 20
- CategoryTheory.WithInitial.equivCommaproof · cited by 16
- CategoryTheory.zeroMulproof · cited by 12
- AugmentedSimplexCategory.inlproof · cited by 9
- AugmentedSimplexCategory.inrproof · cited by 9
- CategoryTheory.WithTerminal.opEquivproof · cited by 8
- TopPair.ofTopCatproof · cited by 8
- CategoryTheory.Limits.IsInitial.uniqueUpToIsoproof · cited by 8
- CategoryTheory.WithInitial.homToproof · cited by 8
- CategoryTheory.Under.equivalenceOfIsInitialproof · cited by 7
- CategoryTheory.Functor.PushoutObjObj.ofIsInitialLeftproof · cited by 6