preserves finite coproducts
A functor preserves finite coproducts when for every finite family of objects in the domain whose coproduct exists, the coproduct also exists in the codomain and the canonical morphism is an isomorphism.
Dual preserves finite products Related cocontinuous, preserves binary coproducts, preserves coproducts, preserves initial objects External nLab link
Relevant implications
Examples
There are 37 functors with this property.
- abelianization functor for groups
- binary coproduct functor on sets
- binary diagonal functor on the category of sets
- countable copower functor on sets
- discrete topology functor
- doubling functor on sets
- empty functor to the category of sets
- enveloping group functor
- forgetful functor for topological spaces
- forgetful functor from finite abelian groups to abelian groups
- forgetful functor from finite groups to groups
- forgetful functor from finite sets to sets
- forgetful functor from groups to monoids
- forgetful functor from Hausdorff spaces to topological spaces
- forgetful functor from torsion abelian groups to abelian groups
- forgetful functor from torsion-free abelian groups to abelian groups
- free group functor
- group of units functor
- identity functor on the category of sets
- inclusion functor from extended natural numbers to ordinal numbers
- modulo p functor
- monoid ring functor
- morphism endpoints inclusion
- nerve functor
- opposite category functor
- opposite monoid functor
- p-torsion functor
- path components functor
- rational product functor
- span endpoints inclusion
- Stone-Čech compactification functor
- torsion functor
- trivial functor from the category of groups
- trivial functor from the category of sets
- trivial functor from the delooping
- trivial functor from the walking idempotent
- walking isomorphism object inclusion
Counterexamples
There are 19 functors without this property.
- binary product functor on sets
- Brauer group functor
- contravariant power set functor
- covariant power set functor
- forgetful functor for groups
- forgetful functor for rings
- forgetful functor for vector spaces
- forgetful functor from abelian groups to groups
- forgetful functor from commutative rings to rings
- forgetful functor from groups to pointed sets
- forgetful functor from rings to monoids
- functor of continuous functions
- fundamental group functor
- indiscrete topology functor
- ring idempotents functor
- sequences functor on sets
- simple-group probing functor
- squaring functor on sets
- walking morphism representation
Unknown
There are 0 functors for which the database has no information on whether they satisfy this property.
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