Theorems · Definition · category theory
CategoryTheory.Limits.BinaryFan.mk
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] → {X Y P : C} → (P ⟶ X) → (P ⟶ Y) → CategoryTheory.Limits.BinaryFan X YA binary fan with vertex P consists of the two projections π₁ : P ⟶ X and π₂ : P ⟶ Y.
- Cited by
- 112 results in Mathlib
- Foundations
- Depth 23 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.
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.Discreteproof · cited by 2,447
- CategoryTheory.Limits.WalkingPairproof · cited by 1,319
- CategoryTheory.Functor.constproof · cited by 1,264
- CategoryTheory.Limits.pairproof · cited by 536
- CategoryTheory.Limits.BinaryFanstatement · cited by 51
Cited by167
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.prod.liftproof · cited by 123
- CategoryTheory.Limits.prod.comp_liftproof · cited by 46
- CategoryTheory.Limits.biprod.lift_sndproof · cited by 33
- CategoryTheory.Limits.biprod.lift_fstproof · cited by 31
- CategoryTheory.Limits.prod.lift_mapproof · cited by 26
- CategoryTheory.Limits.pullbackConeEquivBinaryFanproof · cited by 23
- CategoryTheory.Limits.BinaryBicone.toConeproof · cited by 18
- CategoryTheory.Limits.BinaryFan.IsLimit.liftproof · cited by 12
- CategoryTheory.Limits.prod.lift_fstproof · cited by 10
- CategoryTheory.Limits.prod.lift_sndproof · cited by 10
- CategoryTheory.Limits.Types.binaryProductConeproof · cited by 8
- HomotopicalAlgebra.PrepathObject.p_fstproof · cited by 7