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Theorems · Definition · category theory

TopCat.Presheaf.pushforwardPullbackAdjunction

Deprecated since 2026-03-03Use TopCat.Presheaf.pullbackPushforwardAdjunction instead.

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasColimits C] →
      {X Y : TopCat} → (f : X ⟶ Y) → TopCat.Presheaf.pullback C f ⊣ TopCat.Presheaf.pushforward C f

Alias of TopCat.Presheaf.pullbackPushforwardAdjunction. The pullback and pushforward along a continuous map are adjoint to each other.

Defined in
Mathlib.Topology.Sheaves.Presheaf
Cited by
0 results in Mathlib
Foundations
Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasColimits
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CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomTopCat · cited by 1889TopCatCategoryTheory.Adjunction · cited by 524CategoryTheory.AdjunctionTopCat.Presheaf · cited by 371TopCat.PresheafTopCat.Presheaf.pushforward · cited by 174Presheaf.pushforwardCategoryTheory.Limits.HasColimits · cited by 139Limits.HasColimitsTopCat.Presheaf.pullback · cited by 19Presheaf.pullbackTopCat.Presheaf.pullbackPushforwardAdjunction · cited by 9Presheaf.pullbackPushforw…Presheaf.pushforwardPullbackA…CITED BYCITES

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