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Theorems · Definition · category theory

CategoryTheory.ObjectProperty.shiftClosure

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    CategoryTheory.ObjectProperty C →
      (A : Type u_2) → [inst_1 : AddMonoid A] → [CategoryTheory.HasShift C A] → CategoryTheory.ObjectProperty C

The closure by shifts and isomorphism of a predicate on objects in a category.

Defined in
Mathlib.CategoryTheory.ObjectProperty.Shift
Cited by
17 results in Mathlib
Foundations
Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryAddMonoidCategoryTheory.HasShift
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Around this declaration

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

CategoryTheory.ObjectProperty.triangEnvelopeIter · cited by 12ObjectProperty.triangEnve…CategoryTheory.ObjectProperty.shiftClosure_eq_self · cited by 4ObjectProperty.shiftClosu…CategoryTheory.ObjectProperty.le_shiftClosure · cited by 3ObjectProperty.le_shiftCl…CategoryTheory.ObjectProperty.monotone_shiftClosure · cited by 2ObjectProperty.monotone_s…CategoryTheory.ObjectProperty.shiftClosure_le_iff · cited by 2ObjectProperty.shiftClosu…CategoryTheory.ObjectProperty.monotone'_triangEnvelopeIter · cited by 1ObjectProperty.monotone'_…CategoryTheory.ObjectProperty.shiftClosure_bot · cited by 1ObjectProperty.shiftClosu…CategoryTheory.ObjectProperty.triangEnvelopeIter_zero · cited by 1ObjectProperty.triangEnve…CategoryTheory.ObjectProperty.le_triangEnvelopeIter · cited by 1ObjectProperty.le_triangE…CategoryTheory.ObjectProperty.triangEnvelopeIter_add · cited by 0ObjectProperty.triangEnve…CategoryTheory.ObjectProperty.shiftClosure_eq_iSup · cited by 0ObjectProperty.shiftClosu…CategoryTheory.ObjectProperty.shiftClosure_top · cited by 0ObjectProperty.shiftClosu…CategoryTheory.ObjectProperty.triangEnvelopeIter_succ · cited by 0ObjectProperty.triangEnve…CategoryTheory.ObjectProperty.triangEnvelopeIter_succ' · cited by 0ObjectProperty.triangEnve…CategoryTheory.ObjectProperty.triangEnvelopeIter_add' · cited by 0ObjectProperty.triangEnve…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Iso · cited by 3963CategoryTheory.IsoAddMonoid · cited by 2864AddMonoidCategoryTheory.shiftFunctor · cited by 1553CategoryTheory.shiftFunct…CategoryTheory.HasShift · cited by 1527CategoryTheory.HasShiftCategoryTheory.ObjectProperty · cited by 798CategoryTheory.ObjectProp…ObjectProperty.shiftClosureCITED BYCITES

Cites7

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Cited by18

Results whose statement or proof uses this declaration.