symmetric monoidal poset of natural numbers

Notation

(\IN,\leq,+,0)

Underlying category partially ordered set of natural numbers External nLab Link

We view the poset $(\IN,\leq)$ as a thin category and equip it with the strict symmetric monoidal structure defined by $a \otimes b \coloneqq a + b$ and the monoidal unit $0$ .

Satisfied Properties

Assigned properties

is strict
is coclosed

Deduced properties

is well-pointed

Unsatisfied Properties

Assigned properties

is not cartesian
is not codistributive
is not distributive
is not cocartesian

Deduced properties*

is not closed
is not finitely cocomplete
is not infinitary distributive
is not trivial
is not finitely complete
is not infinitary codistributive
is not cocomplete
is not complete
is not self-dual

*This also uses the deduced satisfied properties.

Unknown properties

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