continuous
A functor is continuous when it preserves all small limits.
- Dual property: cocontinuous
- nLab Link
Relevant implications
- cofinitary andleft exact implies continuous *
- continuous implies cofinitary andequalizer-preserving andproduct-preserving
- continuous implies right adjoint *
- equalizer-preserving andproduct-preserving implies continuous *
- equivalence implies continuous andmonadic andright adjoint
- representable implies continuous
- right adjoint implies continuous
*Those implications also require assumptions on the source or target category.
Examples
There are 3 functors with this property.
- contravariant power set functor
- forgetful functor for vector spaces
- identity functor on the category of sets
Counterexamples
There are 3 functors without this property.
Unknown
There are 0 functors for which the database has no information on whether they satisfy this property.
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