Implication Details
Claim: If a category is cartesian closed and has countable coproducts, then it is countably distributive.
Proof: Each functor is left adjoint and hence preserves countable coproducts (in fact, all colimits).
Show 10 categories using this implication
- category of combinatorial species
- category of compact Hausdorff spaces
- category of finite sets
- category of semigroups
- partially ordered set of extended natural numbers
- preordered set of integers w.r.t. divisibility
- real interval [0,1]
- walking commutative square
- walking composable pair
- walking morphism