Implication Details
Claim: Given a symmetric monoidal category whose underlying category has coproducts, if it is closed, then it is infinitary distributive.
Proof: Each functor is a left adjoint and therefore preserves coproducts.
This implication has a dual.
Show 5 symmetric monoidal categories using this implication
- trivial symmetric monoidal category
- symmetric monoidal category of abelian groups
- 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