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Theorems · Definition · category theory

CategoryTheory.Functor.diag

(C : Type u₃) → [inst : CategoryTheory.Category.{v₃, u₃} C] → CategoryTheory.Functor C (C × C)

The diagonal functor.

Defined in
Mathlib.CategoryTheory.Products.Basic
Cited by
36 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext
Assumes
CategoryTheory.Category

Around this declaration

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

CategoryTheory.StructuredArrow.ofDiagEquivalence.functor · cited by 6ofDiagEquivalence.functorCategoryTheory.Limits.IsColimit.tensor · cited by 6IsColimit.tensorCategoryTheory.CostructuredArrow.ofDiagEquivalence.functor · cited by 6ofDiagEquivalence.functorCategoryTheory.IsSiftedOrEmpty · cited by 4CategoryTheory.IsSiftedOr…CategoryTheory.StructuredArrow.ofDiagEquivalence.inverse · cited by 4ofDiagEquivalence.inverseCategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse · cited by 4ofDiagEquivalence.inverseCategoryTheory.MonoidalCategory.externalProductCompDiagIso · cited by 3MonoidalCategory.external…CategoryTheory.IsSifted.isSiftedOrEmpty_of_colim_preservesBinaryProducts · cited by 1IsSifted.isSiftedOrEmpty_…CategoryTheory.CostructuredArrow.ofDiagEquivalence.inverse_obj_right_as · cited by 0ofDiagEquivalence.inverse…CategoryTheory.IsSifted.casesOn · cited by 0IsSifted.casesOnCategoryTheory.IsSifted.factorization_prodComparison_colim · cited by 0IsSifted.factorization_pr…CategoryTheory.IsSifted.recOn · cited by 0IsSifted.recOnCategoryTheory.Functor.prod'_δ_fst · cited by 0Functor.prod'_δ_fstCategoryTheory.Functor.prod'_δ_snd · cited by 0Functor.prod'_δ_sndCategoryTheory.Functor.prod'_η_fst · cited by 0Functor.prod'_η_fstCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.id · cited by 3333Functor.idCategoryTheory.Functor.prod' · cited by 31Functor.prod'Functor.diagCITED BYCITES

Cites4

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Cited by49

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