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Theorems · Definition · category theory

CategoryTheory.MonoOver.imageForgetAdj

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {X : C} →
      [inst_1 : CategoryTheory.Limits.HasImages C] → CategoryTheory.MonoOver.image ⊣ CategoryTheory.MonoOver.forget X

MonoOver.image : Over X ⥤ MonoOver X is left adjoint to MonoOver.forget : MonoOver X ⥤ Over X

Defined in
Mathlib.CategoryTheory.Subobject.MonoOver
Cited by
0 results in Mathlib
Foundations
Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasImages
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Around this declaration

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

CategoryTheory.MonoOver.existsPullbackAdj · cited by 0MonoOver.existsPullbackAdjCategoryTheory.MonoOver.forgetImage · cited by 0MonoOver.forgetImageCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.ObjectProperty.FullSubcategory.obj · cited by 1316FullSubcategory.objCategoryTheory.Over · cited by 935CategoryTheory.OverCategoryTheory.InducedCategory.Hom.hom · cited by 850Hom.homCategoryTheory.Over.left · cited by 541Over.leftCategoryTheory.Adjunction · cited by 524CategoryTheory.AdjunctionCategoryTheory.Over.hom · cited by 370Over.homCategoryTheory.Over.Hom.left · cited by 287Hom.leftCategoryTheory.MonoOver · cited by 115CategoryTheory.MonoOverCategoryTheory.Over.homMk · cited by 115Over.homMkCategoryTheory.Over.isMono · cited by 111Over.isMonoCategoryTheory.Limits.factorThruImage · cited by 55Limits.factorThruImageMonoOver.imageForgetAdjCITED BYCITES

Cites22

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Cited by2

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