Structures · Category theory
CategoryTheory.Limits.ReflectsColimitsOfSize
A functor F : C ⥤ D reflects colimits if
whenever the image of a cocone over some K : J ⥤ C under F is a colimit cocone in D,
the cocone was already a colimit cocone in C.
Note that we do not assume a priori that D actually has any colimits.
- Shape
- One type argument · adds reflectsColimitsOfShape
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Concrete types that are instances1
- Rep
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Assumed by19
- CategoryTheory.Limits.reflectsColimitsOfSize_of_univLE
- CategoryTheory.Limits.reflectsColimitsOfSize_shrink
- CategoryTheory.Limits.ReflectsColimits.reflectsFilteredColimits
- CategoryTheory.Limits.reflectsLimitsOfSize_leftOp
- CategoryTheory.Limits.instReflectsFiniteColimitsOfReflectsColimitsOfSize
- CategoryTheory.Limits.reflectsColimits_of_natIso
- CategoryTheory.Limits.reflectsLimitsOfSize_op
- CategoryTheory.Limits.reflectsLimitsOfSize_of_rightOp
- CategoryTheory.Limits.reflectsLimitsOfSize_rightOp
- CategoryTheory.Limits.comp_reflectsColimits
- CategoryTheory.Limits.reflectsSmallestColimits_of_reflectsColimits
- CategoryTheory.Limits.reflectsLimitsOfSize_of_unop
- CategoryTheory.Limits.reflectsLimitsOfSize_of_leftOp
- CategoryTheory.Limits.ReflectsColimitsOfSize.reflectsFiniteColimits
- CategoryTheory.Limits.reflectsLimitsOfSize_of_op
- CategoryTheory.Limits.reflectsColimitsOfShape_of_reflectsColimits
- CategoryTheory.Limits.reflectsLimitsOfSize_unop
- CategoryTheory.Limits.ReflectsColimitsOfSize.reflectsColimitsOfShape
- CategoryTheory.Limits.preservesColimits_of_reflects_of_preserves
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