delooping of the additive monoid of natural numbers

  • notation: BNB\mathbb{N}
  • objects: a single object
  • morphisms: the natural numbers, with addition serving as composition
  • Related categories: BGBG, BOnB\mathbf{On}

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 = (\mathbb{N},+,0), so composition is n∘m=n+mn \circ m = n + m.

Satisfied Properties

Properties from the database

Deduced properties

Unsatisfied Properties

Properties from the database

Deduced properties*

*This also uses the deduced satisfied properties.

Unknown properties

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Special objects

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Special morphisms

  • isomorphisms: only the number 00
  • monomorphisms: every morphism
  • epimorphisms: every morphism
  • regular monomorphisms: same as isomorphisms
  • regular epimorphisms: same as isomorphisms