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Theorems · Definition · category theory

CategoryTheory.ObjectProperty.map

{C : Type u} →
  {D : Type u'} →
    [inst : CategoryTheory.Category.{v, u} C] →
      [inst_1 : CategoryTheory.Category.{v', u'} D] →
        CategoryTheory.ObjectProperty C → CategoryTheory.Functor C D → CategoryTheory.ObjectProperty D

The essential image of a property of objects by a functor.

Defined in
Mathlib.CategoryTheory.ObjectProperty.Basic
Cited by
15 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.Category

Around this declaration

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

CategoryTheory.Adjunction.hasCardinalFilteredGenerator · cited by 3Adjunction.hasCardinalFil…CategoryTheory.Adjunction.isCardinalFilteredGenerator · cited by 1Adjunction.isCardinalFilt…CategoryTheory.IsCardinalFilteredGenerator.of_isDense · cited by 1IsCardinalFilteredGenerat…CategoryTheory.IsCardinalFilteredGenerator.of_isDense_ι · cited by 1IsCardinalFilteredGenerat…CategoryTheory.ObjectProperty.prop_map_obj · cited by 1ObjectProperty.prop_map_o…CategoryTheory.ObjectProperty.EssentiallySmall.of_functor · cited by 1EssentiallySmall.of_funct…CategoryTheory.ObjectProperty.strictMap_le_map · cited by 1ObjectProperty.strictMap_…CategoryTheory.ObjectProperty.ι_map_top · cited by 1ObjectProperty.ι_map_topCategoryTheory.ObjectProperty.map_monotone · cited by 1ObjectProperty.map_monoto…CategoryTheory.ObjectProperty.map_top · cited by 0ObjectProperty.map_topCategoryTheory.MorphismProperty.ofObjectProperty_map_le · cited by 0MorphismProperty.ofObject…CategoryTheory.ObjectProperty.prop_map_iff · cited by 0ObjectProperty.prop_map_i…CategoryTheory.ObjectProperty.isoClosure_strictMap · cited by 0ObjectProperty.isoClosure…CategoryTheory.Functor.essImage_ι_comp · cited by 0Functor.essImage_ι_compCategoryTheory.ObjectProperty.map_isoClosure · cited by 0ObjectProperty.map_isoClo…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.ObjectProperty · cited by 798CategoryTheory.ObjectProp…ObjectProperty.mapCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by15

Results whose statement or proof uses this declaration.