delooping of the additive monoid of ordinal numbers

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

Every monoid MM induces a category BMBM with a single object ∗*. This also works when MM is large, in which case BMBM is not locally small. In this example, we apply this construction to the large monoid of ordinal numbers with respect to addition, so composition is α∘β=α+β\alpha \circ \beta = \alpha + \beta.

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 ordinal 00
  • monomorphisms: every ordinal number
  • epimorphisms: finite ordinal numbers
  • regular monomorphisms: ordinals of the form α⋅ω\alpha \cdot \omega, where α\alpha is any ordinal
  • regular epimorphisms: same as isomorphisms