Implication Details
Claim: Given a symmetric monoidal category whose underlying category is cocomplete, if it is closed, then it is cocomplete.
Proof: Each functor is a left adjoint and therefore preserves colimits.
This implication has a dual.
Show 6 symmetric monoidal categories using this implication
- symmetric monoidal category of abelian groups
- cartesian symmetric monoidal category of small categories
- 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