Theorems · Definition · category theory

CategoryTheory.Limits.pair

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    C → C → CategoryTheory.Functor (CategoryTheory.Discrete CategoryTheory.Limits.WalkingPair) C

The diagram on the walking pair, sending the two points to X and Y.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
Cited by: 536 results in Mathlib
Foundations: Depth 13 from the axioms, rests on 72 definitions · uses propext
Assumes: CategoryTheory.Category

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites6

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.Functorstatement · cited by 16,252
CategoryTheory.Discretestatement · cited by 2,447
CategoryTheory.Limits.WalkingPairstatement and proof · cited by 1,319
CategoryTheory.Discrete.functorproof · cited by 633
CategoryTheory.Limits.WalkingPair.casesOnproof · cited by 59

Cited by773

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.prodproof · cited by 364
CategoryTheory.Limits.coprodproof · cited by 252
CategoryTheory.Limits.prod.fstproof · cited by 189
CategoryTheory.Limits.prod.sndproof · cited by 185
CategoryTheory.Limits.HasBinaryProductproof · cited by 169
CategoryTheory.Limits.coprod.inlproof · cited by 137
CategoryTheory.Limits.coprod.inrproof · cited by 132
CategoryTheory.Limits.prod.liftproof · cited by 123
CategoryTheory.Limits.BinaryFan.mkproof · cited by 112
CategoryTheory.Limits.BinaryCofan.mkproof · cited by 83
CategoryTheory.Limits.HasBinaryCoproductproof · cited by 81
CategoryTheory.Limits.coprod.descproof · cited by 69

Showing the 200 most cited of 773.