symmetric monoidal category of abelian groups
- Notation:
- Underlying category: category of abelian groups
- Parent:
- Related symmetric monoidal categories:
- nLab Link
This is the category of abelian groups equipped with the usual tensor product of abelian groups and the monoidal unit . It is the special case of where .
Satisfied Properties
Assigned properties
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Deduced properties
- is closed
- is well-pointed
- is cocomplete
- is finitely cocomplete
- is distributive
- is infinitary distributive
- is codistributive
Unsatisfied Properties
Assigned properties
- is not finitely complete
Deduced properties*
- is not infinitary codistributive
- is not strict
- is not coclosed
- is not complete
- is not self-dual
- is not trivial
- is not cartesian
- is not cocartesian
*This also uses the deduced satisfied properties.
Unknown properties
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Indistinguishable symmetric monoidal categories
These symmetric monoidal categories in the database currently have exactly the same properties as the symmetric monoidal category of abelian groups. This indicates that the data may be incomplete or that a distinguishing property may be missing from the database.