Theorems · Definition · category theory
CategoryTheory.Limits.BinaryFan.IsLimit.lift
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{X Y W : C} →
{s : CategoryTheory.Limits.BinaryFan X Y} → CategoryTheory.Limits.IsLimit s → (W ⟶ X) → (W ⟶ Y) → (W ⟶ s.pt)If s is a limit binary fan over X and Y, then every pair of morphisms f : W ⟶ X and
g : W ⟶ Y induces a morphism l : W ⟶ s.pt satisfying l ≫ s.fst = f and l ≫ s.snd = g.
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.Discretestatement · cited by 2,447
- CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
- CategoryTheory.Limits.Cone.ptstatement · cited by 1,298
- CategoryTheory.Limits.IsLimitstatement and proof · cited by 664
- CategoryTheory.Limits.pairstatement · cited by 536
- CategoryTheory.Limits.IsLimit.liftproof · cited by 167
- CategoryTheory.Limits.BinaryFan.mkproof · cited by 112
- CategoryTheory.Limits.BinaryFanstatement and proof · cited by 51
Cited by19
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.biprod.liftproof · cited by 79
- CategoryTheory.Limits.BinaryBicone.ofLimitConeproof · cited by 7
- CategoryTheory.Limits.BinaryFan.assocInvproof · cited by 6
- isPullbackOfIsTerminalIsProductproof · cited by 3
- CategoryTheory.Limits.Types.binaryProductFunctorproof · cited by 3
- CategoryTheory.Limits.BinaryFan.IsLimit.lift_fststatement · cited by 2
- CategoryTheory.Limits.BinaryFan.IsLimit.lift_sndstatement · cited by 2
- CategoryTheory.Limits.BinaryFan.isLimitFlipproof · cited by 1
- CategoryTheory.Limits.inl_of_isLimitstatement · cited by 0
- CategoryTheory.isPullback_iff_isLimit_binaryFan_of_isThinproof · cited by 0
- CategoryTheory.Limits.BinaryFan.assocInv_fststatement · cited by 0
- CategoryTheory.Limits.BinaryBicone.ofLimitCone_inlstatement · cited by 0