well-copointed
A symmetric monoidal category is called well-copointed if the monoidal unit is a cogenerator. Equivalently, the functor is faithful.
Relevant implications
- implies well-copointed
Examples
There are 4 symmetric monoidal categories with this property.
- symmetric monoidal category of finite-dimensional vector spaces
- symmetric monoidal category of vector spaces
- symmetric monoidal poset of natural numbers
- trivial symmetric monoidal category
Counterexamples
There are 6 symmetric monoidal categories without this property.
- cartesian symmetric monoidal category of sets
- cartesian symmetric monoidal category of small categories
- cartesian symmetric monoidal category of topological spaces
- cocartesian symmetric monoidal category of sets
- symmetric monoidal category of abelian groups
- symmetric monoidal category of finitely generated abelian groups
Undecidable symmetric monoidal categories
There are 3 symmetric monoidal categories for which it cannot be decided whether this property is satisfied.
- symmetric monoidal category of modules over a commutative ring
- symmetric monoidal category of modules over a non-absolutely flat commutative ring
- symmetric monoidal category of modules over an absolutely flat commutative ring
Unknown
There are 0 symmetric monoidal categories for which the database has no information on whether they satisfy this property.
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