Theorems · Definition · category theory
CategoryTheory.Limits.initial.to
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] → [inst_1 : CategoryTheory.Limits.HasInitial C] → (P : C) → ⊥_ C ⟶ PThe map to an object from the initial object.
- Cited by
- 63 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.HasInitialstatement and proof · cited by 185
- CategoryTheory.Functor.emptyproof · cited by 103
- CategoryTheory.Limits.initialstatement · cited by 84
- CategoryTheory.Limits.colimit.descproof · cited by 63
- CategoryTheory.Limits.asEmptyCoconeproof · cited by 6
Cited by78
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.IsCofibrantproof · cited by 56
- CategoryTheory.Limits.initialIsInitialproof · cited by 35
- CategoryTheory.Limits.initial.to_compstatement and proof · cited by 11
- coprodIsoPushoutstatement · cited by 8
- colimitCoconeOfInitialAndPushoutsproof · cited by 6
- CategoryTheory.Limits.coprod.leftUnitorproof · cited by 4
- CategoryTheory.Limits.coprod.rightUnitorproof · cited by 4
- CategoryTheory.MonoOver.initialTo_b_eq_zerostatement · cited by 3
- HomotopicalAlgebra.RightHomotopyRel.exists_very_good_pathObjectproof · cited by 3
- CategoryTheory.Limits.colimitConstInitialproof · cited by 3
- HomotopicalAlgebra.isCofibrant_of_cofibrationproof · cited by 3