nLab closed midpoint algebra

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Definition

Definition

A closed midpoint algebra is a cancellative midpoint algebra (M,|)(M,\vert) equipped with a pair of elements ,:M\bot, \top \colon M.

In other words, it is a bi-pointed cancellative midpoint algebra.

This Def. may be gleaned from the second half of footnote 28 of Freyd 2008, where it is described as a fragment of the definition of “scale” given in Section 2 there.

Properties

Proposition

The initial object among closed midpoint algebras (Def. ) is the unit interval in the dyadic rational numbers.

References

  • Peter Freyd: Algebraic real analysis, Theory and Applications of Categories 20* 10 (2008) 215–306 [tac:20-10, pdf]

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