preserves terminal objects
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: preserves initial objects
- Related properties: continuous, preserves finite products
- nLab Link
Relevant implications
Examples
There are 21 functors with this property.
- abelianization functor for groups
- binary diagonal functor on the category of sets
- binary product functor on sets
- contravariant power set functor
- discrete topology functor
- enveloping group functor
- forgetful functor for groups
- forgetful functor for rings
- forgetful functor for topological spaces
- forgetful functor for vector spaces
- forgetful functor from abelian groups to groups
- forgetful functor from groups to monoids
- forgetful functor from rings to monoids
- functor of continuous functions
- group of units functor
- identity functor on the category of sets
- modulo p functor
- p-torsion functor
- sequences functor on sets
- squaring functor on sets
- torsion functor
Counterexamples
There are 6 functors without this property.
- binary coproduct functor on sets
- countable copower functor on sets
- covariant power set functor
- doubling functor on sets
- free group functor
- monoid ring functor
Unknown
There are 0 functors for which the database has no information on whether they satisfy this property.
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