delooping of the additive monoid of natural numbers

 category theory  number theory
Notation BNB\IN Objects a single object Morphisms the natural numbers, with addition serving as composition Related BGBG, BOnB\OnColl, BCBC, BDBD, Setc,∞\Set_{\c,\infty}
Every monoid MM induces a category BMBM with a single object ∗*, morphisms given by the elements of MM, and composition given by the monoid operation. Some of the properties of this category depend on the specific monoid. In this example, we take the commutative monoid M=(N,+,0)M = (\IN,+,0), so composition is n∘m=n+mn \circ m = n + m.

Satisfied properties

Assigned properties

Deduced properties

Unsatisfied properties

Assigned properties

Deduced properties*

*This also uses the deduced satisfied properties.

Unknown properties

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Special objects

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Special morphisms