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Theorems · Definition · category theory

CategoryTheory.MonoOver.mapPullbackAdj

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {X Y : C} →
      [inst_1 : CategoryTheory.Limits.HasPullbacks C] →
        (f : X ⟶ Y) →
          [inst_2 : CategoryTheory.Mono f] → CategoryTheory.MonoOver.map f ⊣ CategoryTheory.MonoOver.pullback f

map f is left adjoint to pullback f when f is a monomorphism

Defined in
Mathlib.CategoryTheory.Subobject.MonoOver
Cited by
0 results in Mathlib
Foundations
Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacksCategoryTheory.Mono
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Around this declaration

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CategoryTheory.MonoOver.pullbackMapSelf · cited by 1MonoOver.pullbackMapSelfCategoryTheory.Subobject.mapPullbackAdj · cited by 0Subobject.mapPullbackAdjCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Over · cited by 935CategoryTheory.OverCategoryTheory.Mono · cited by 893CategoryTheory.MonoCategoryTheory.Iso.refl · cited by 727Iso.reflCategoryTheory.Adjunction · cited by 524CategoryTheory.AdjunctionCategoryTheory.Limits.HasPullbacks · cited by 439Limits.HasPullbacksCategoryTheory.MonoOver · cited by 115CategoryTheory.MonoOverCategoryTheory.Over.isMono · cited by 111Over.isMonoCategoryTheory.Over.map · cited by 97Over.mapCategoryTheory.Over.pullback · cited by 53Over.pullbackCategoryTheory.MonoOver.forget · cited by 23MonoOver.forgetCategoryTheory.MonoOver.map · cited by 12MonoOver.mapCategoryTheory.Over.mapPullbackAdj · cited by 8Over.mapPullbackAdjMonoOver.mapPullbackAdjCITED BYCITES

Cites18

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Cited by2

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