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Theorems · Definition · category theory

CategoryTheory.Limits.mapPair

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {F G : CategoryTheory.Functor (CategoryTheory.Discrete CategoryTheory.Limits.WalkingPair) C} →
      (F.obj { as := CategoryTheory.Limits.WalkingPair.left } ⟶
          G.obj { as := CategoryTheory.Limits.WalkingPair.left }) →
        (F.obj { as := CategoryTheory.Limits.WalkingPair.right } ⟶
            G.obj { as := CategoryTheory.Limits.WalkingPair.right }) →
          (F ⟶ G)

The natural transformation between two functors out of the walking pair, specified by its components.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts
Cited by
18 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
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Around this declaration

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

CategoryTheory.Limits.prod.map · cited by 105prod.mapCategoryTheory.Limits.coprod.map · cited by 49coprod.mapCategoryTheory.Limits.prod.map_snd · cited by 31prod.map_sndCategoryTheory.Limits.biprod.map · cited by 27biprod.mapCategoryTheory.Limits.prod.map_fst · cited by 27prod.map_fstCategoryTheory.Limits.coprod.inl_map · cited by 11coprod.inl_mapCategoryTheory.Limits.coprod.inr_map · cited by 10coprod.inr_mapCategoryTheory.Limits.biprod.map_fst · cited by 6biprod.map_fstCategoryTheory.Limits.biprod.map_snd · cited by 5biprod.map_sndCategoryTheory.Limits.biprod.inl_map · cited by 3biprod.inl_mapCategoryTheory.Limits.biprod.inr_map · cited by 3biprod.inr_mapCategoryTheory.BinaryCofan.isVanKampen_iff · cited by 2BinaryCofan.isVanKampen_i…CategoryTheory.isUniversalColimit_extendCofan · cited by 2CategoryTheory.isUniversa…CategoryTheory.Limits.biprod.map_eq_map' · cited by 2biprod.map_eq_map'CategoryTheory.BinaryCofan.isPullback_initial_to_of_isVanKampen · cited by 1BinaryCofan.isPullback_in…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteCategoryTheory.Limits.WalkingPair · cited by 1319Limits.WalkingPairLimits.mapPairCITED BYCITES

Cites6

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Cited by22

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