Implication Details
Claim: Given a symmetric monoidal category whose underlying category is finitely cocomplete, if it is closed, then it is finitely cocomplete.
Proof: Each functor is a left adjoint and therefore preserves finite colimits.
This implication has a dual.
Show 10 symmetric monoidal categories using this implication
- trivial symmetric monoidal category
- symmetric monoidal category of finitely generated abelian groups
- symmetric monoidal category of abelian groups
- cartesian symmetric monoidal category of small categories
- symmetric monoidal category of finite-dimensional vector spaces
- symmetric monoidal category of modules over a commutative ring
- symmetric monoidal category of modules over an absolutely flat commutative ring
- symmetric monoidal category of modules over a non-absolutely flat commutative ring
- cartesian symmetric monoidal category of sets
- cartesian symmetric monoidal category of topological spaces