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Theorems · Definition · category theory

CategoryTheory.Subfunctor.equivalenceMonoOver

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (F : CategoryTheory.Functor C (Type w)) → CategoryTheory.Subfunctor F ≌ CategoryTheory.MonoOver F

The equivalence of categories Subfunctor F ≌ MonoOver F.

Defined in
Mathlib.CategoryTheory.Subfunctor.Subobject
Cited by
8 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.Subfunctor.range_subobjectMk_ι · cited by 0Subfunctor.range_subobjec…CategoryTheory.Subfunctor.subobjectMk_range_arrow · cited by 0Subfunctor.subobjectMk_ra…CategoryTheory.Subfunctor.equivalenceMonoOver_counitIso · cited by 0Subfunctor.equivalenceMon…CategoryTheory.Subfunctor.equivalenceMonoOver_functor_map · cited by 0Subfunctor.equivalenceMon…CategoryTheory.Subfunctor.equivalenceMonoOver_functor_obj · cited by 0Subfunctor.equivalenceMon…CategoryTheory.Subfunctor.equivalenceMonoOver_inverse_map · cited by 0Subfunctor.equivalenceMon…CategoryTheory.Subfunctor.equivalenceMonoOver_inverse_obj · cited by 0Subfunctor.equivalenceMon…CategoryTheory.Subfunctor.equivalenceMonoOver_unitIso · cited by 0Subfunctor.equivalenceMon…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Iso.symm · cited by 993Iso.symmCategoryTheory.Over · cited by 935CategoryTheory.OverCategoryTheory.Equivalence · cited by 601CategoryTheory.EquivalenceCategoryTheory.homOfLE · cited by 554CategoryTheory.homOfLECategoryTheory.NatIso.ofComponents · cited by 178NatIso.ofComponentsCategoryTheory.asIso · cited by 177CategoryTheory.asIsoCategoryTheory.MonoOver · cited by 115CategoryTheory.MonoOverCategoryTheory.Subfunctor · cited by 112CategoryTheory.SubfunctorCategoryTheory.Over.isMono · cited by 111Over.isMonoCategoryTheory.eqToIso · cited by 97CategoryTheory.eqToIsoCategoryTheory.Subfunctor.ι · cited by 50Subfunctor.ιCategoryTheory.Subfunctor.range · cited by 46Subfunctor.rangeSubfunctor.equivalenceMonoOverCITED BYCITES

Cites21

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Cited by8

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