CatDat

Symmetric monoidal category implications

Found 15 implications*

• cartesian andcodistributive implies trivial
• cartesian () implies closed
• cartesian () implies distributive
• cartesian () implies infinitary distributive
• closed () implies cocomplete
• closed () implies distributive
• closed () implies finitely cocomplete
• closed () implies infinitary distributive
• cocomplete implies finitely cocomplete andinfinitary distributive
• distributive () implies codistributive
• finitely cocomplete implies distributive
• infinitary distributive implies distributive
• trivial implies cartesian andclosed andcocomplete andself-dual
• trivial implies well-pointed
• () implies well-pointed

*Deductions from these implications are automatically incorporated into each symmetric monoidal category whenever applicable. Moreover, implications are automatically dualized when the corresponding dual properties exist.

For results that do not quite fit the implication model, content pages are used instead.