Theorems · Definition · category theory
CategoryTheory.Prod.fst
(C : Type u₁) →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
(D : Type u₂) → [inst_1 : CategoryTheory.Category.{v₂, u₂} D] → CategoryTheory.Functor (C × D) Cfst is the functor (X, Y) ↦ X.
- Defined in
- Mathlib.CategoryTheory.Products.Basic
- Cited by
- 51 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.Homproof · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
Cited by73
Results whose statement or proof uses this declaration.
- CategoryTheory.Join.mapPairproof · cited by 58
- CategoryTheory.Join.opEquivproof · cited by 18
- CategoryTheory.Join.mkFunctorstatement and proof · cited by 16
- CategoryTheory.Join.edgeTransformstatement and proof · cited by 13
- CategoryTheory.functorProdToProdFunctorproof · cited by 11
- CategoryTheory.Join.mkNatTransstatement and proof · cited by 9
- CategoryTheory.Join.mapPairLeftproof · cited by 6
- CategoryTheory.Join.mapPairRightproof · cited by 6
- CategoryTheory.Join.mkNatTrans.congr_simpstatement and proof · cited by 4
- CategoryTheory.Functor.prod'CompFststatement and proof · cited by 4
- CategoryTheory.Pi.optionEquivalenceproof · cited by 4
- CategoryTheory.Join.mkNatIsostatement and proof · cited by 3