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Theorems · Definition · category theory

CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.toTransfiniteCompositionOfShape

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {W : CategoryTheory.MorphismProperty C} →
      {J : Type w} →
        [inst_1 : LinearOrder J] →
          [inst_2 : SuccOrder J] →
            [inst_3 : OrderBot J] →
              [inst_4 : WellFoundedLT J] →
                {X Y : C} →
                  {f : X ⟶ Y} → W.TransfiniteCompositionOfShape J f → CategoryTheory.TransfiniteCompositionOfShape J f
Defined in
Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition
Cited by
24 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext
Assumes
CategoryTheory.CategoryLinearOrderSuccOrderOrderBotWellFoundedLT

Around this declaration

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

CategoryTheory.OrthogonalReflection.iteration · cited by 6OrthogonalReflection.iter…CategoryTheory.SmallObject.iterationFunctorObjObjRightIso · cited by 4SmallObject.iterationFunc…CategoryTheory.SmallObject.relativeCellComplexιObj · cited by 4SmallObject.relativeCellC…CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofLE · cited by 3TransfiniteCompositionOfS…CategoryTheory.SmallObject.transfiniteCompositionOfShapeιIterationAppRight · cited by 3SmallObject.transfiniteCo…CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ici · cited by 2TransfiniteCompositionOfS…CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right · cited by 2SmallObject.iterationFunc…CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.map_mem · cited by 2TransfiniteCompositionOfS…CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.map · cited by 2TransfiniteCompositionOfS…CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofOrderIso · cited by 2TransfiniteCompositionOfS…CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.iic · cited by 1TransfiniteCompositionOfS…CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofArrowIso · cited by 1TransfiniteCompositionOfS…CategoryTheory.SmallObject.πFunctorObj_eq · cited by 1SmallObject.πFunctorObj_eqCategoryTheory.MorphismProperty.IsStableUnderTransfiniteCompositionOfShape.of_isStableUnderColimitsOfShape.mem · cited by 1of_isStableUnderColimitsO…CategoryTheory.MorphismProperty.IsStableUnderTransfiniteCompositionOfShape.of_isStableUnderColimitsOfShape.mem_map_bot_le · cited by 1of_isStableUnderColimitsO…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomLinearOrder · cited by 8572LinearOrderCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…OrderBot · cited by 1055OrderBotSuccOrder · cited by 574SuccOrderWellFoundedLT · cited by 491WellFoundedLTCategoryTheory.TransfiniteCompositionOfShape · cited by 32CategoryTheory.Transfinit…CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape · cited by 20MorphismProperty.Transfin…TransfiniteCompositionOfShape…CITED BYCITES

Cites9

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Cited by34

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