terminal-object-preserving
A functor preserves terminal objects when it maps every terminal object to a terminal object. It is not assumed that the source category has a terminal object.
- Dual property: initial-object-preserving
Relevant implications
- finite-product-preserving implies terminal-object-preserving
- left exact implies finite-product-preserving andterminal-object-preserving
*Those implications also require assumptions on the source or target category.
Examples
There are 4 functors with this property.
- abelianization functor for groups
- contravariant power set functor
- forgetful functor for vector spaces
- identity functor on the category of sets
Counterexamples
There are 2 functors without this property.
Unknown
There are 0 functors for which the database has no information on whether they satisfy this property.
—