Structures · Category theory
CategoryTheory.Limits.ReflectsLimitsOfSize
A functor F : C ⥤ D reflects limits if
whenever the image of a cone over some K : J ⥤ C under F is a limit cone in D,
the cone was already a limit cone in C.
Note that we do not assume a priori that D actually has any limits.
- Shape
- One type argument · adds reflectsLimitsOfShape
Extends0
Extends nothing: this is a root of the hierarchy.
Extended by0
Nothing extends this class yet.
Concrete types that are instances3
- ModuleCat
- Rep
- Opposite
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Assumed by20
- CategoryTheory.Presheaf.isSheaf_of_isSheaf_comp
- CategoryTheory.Limits.reflectsLimitsOfSize_of_univLE
- CategoryTheory.Limits.reflectsLimitsOfSize_shrink
- CategoryTheory.Limits.reflectsSmallestLimits_of_reflectsLimits
- CategoryTheory.Limits.reflectsColimitsOfSize_of_leftOp
- CategoryTheory.Limits.ReflectsLimitsOfSize.reflectsFiniteLimits
- CategoryTheory.Limits.comp_reflectsLimits
- CategoryTheory.Limits.instReflectsFiniteLimitsOfReflectsLimitsOfSize
- CategoryTheory.Limits.reflectsColimitsOfSize_of_op
- CategoryTheory.Limits.reflectsColimitsOfSize_of_unop
- CategoryTheory.Limits.ReflectsLimits.reflectsCofilteredLimits
- CategoryTheory.Limits.ReflectsLimitsOfSize.reflectsLimitsOfShape
- CategoryTheory.Limits.reflectsLimits_of_natIso
- CategoryTheory.Limits.reflectsColimitsOfSize_rightOp
- CategoryTheory.Limits.reflectsColimitsOfSize_leftOp
- CategoryTheory.Limits.reflectsColimitsOfSize_unop
- CategoryTheory.Limits.preservesLimits_of_reflects_of_preserves
- CategoryTheory.Limits.reflectsColimitsOfSize_of_rightOp
- CategoryTheory.Limits.reflectsLimitsOfShape_of_reflectsLimits
- CategoryTheory.Limits.reflectsColimitsOfSize_op
Ancestors0
No ancestors.