cofinitary
A functor is cofinitary when it preserves cofiltered limits.
- Dual property: finitary
Relevant implications
- cofinitary andfinite-product-preserving implies product-preserving *
- cofinitary andleft exact implies continuous *
- continuous implies cofinitary andequalizer-preserving andproduct-preserving
*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 is 1 functor without this property.
Unknown
There are 2 functors for which the database has no information on whether they satisfy this property. Please help us fill in the gaps by contributing to this project.