Theorems · Definition · category theory

CategoryTheory.Limits.prod.fst

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y : C} → [inst_1 : CategoryTheory.Limits.HasBinaryProduct X Y] → X ⨯ Y ⟶ X

The projection map to the first component of the product.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
Cited by: 189 results in Mathlib
Foundations: Depth 24 from the axioms, rests on 137 definitions · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasBinaryProduct

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
Quiver.Homstatement · cited by 32,603
CategoryTheory.Limits.pairproof · cited by 536
CategoryTheory.Limits.prodstatement · cited by 364
CategoryTheory.Limits.limit.πproof · cited by 278
CategoryTheory.Limits.HasBinaryProductstatement and proof · cited by 169

Cited by215

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.prod.comp_liftproof · cited by 46
CategoryTheory.Dial.tensorObjImplproof · cited by 35
CategoryTheory.Limits.prod.hom_extstatement and proof · cited by 33
CategoryTheory.Limits.prod.map_fststatement · cited by 27
CategoryTheory.Limits.prod.lift_mapproof · cited by 26
CategoryTheory.Limits.prodComparisonproof · cited by 26
CategoryTheory.prodComonadproof · cited by 20
CategoryTheory.Limits.opProdIsoCoprodproof · cited by 16
CategoryTheory.Limits.pullbackProdFstIsoProdstatement and proof · cited by 12
CategoryTheory.Limits.prod.braidingproof · cited by 11
CategoryTheory.Limits.pullbackProdSndIsoProdproof · cited by 10
CategoryTheory.Limits.prod.lift_fststatement · cited by 10

Showing the 200 most cited of 215.