Appl Categor Struct
Inﬁnitary Addition, Real Numbers, and Taut Monads
· Ross Street
Received: 31 December 2017 / Accepted: 6 April 2018
© Springer Science+Business Media B.V., part of Springer Nature 2018, corrected publication May 2018
Abstract We make various observations on inﬁnitary addition in the context of the series
monoids introduced in our previous paper on real sets. In particular, we explore additional
conditions on such monoids suggested by Tarski’s Arithmetic of Cardinal Algebras,and
present a monad-theoretic construction that generalizes our construction of paradoxical real
Keywords Inﬁnitary addition · Series monoid · Commutative monoid · Summation ·
Positive reals · Cardinal algebra · Taut monad · Lextensive category · Monoidal category
Mathematics Subject Classiﬁcation 08A65 · 18C15 · 20M14 · 20M50 · 40C99 · 18D10
The original version of this article was revised: In the original publication of the article, Eq. 3.24 was
published incorrectly. The equation was corrected in the article.
Dedicated to Bob Lowen, creator of APCS.
Communicated by Maria Manuel Clementino.
George Janelidze gratefully acknowledges the support of the South African National Research Foundation.
Ross Street gratefully acknowledges the support of Australian Research Council Discovery Grants
DP1094883, DP130101969 and DP160101519.
Department of Mathematics and Applied Mathematics, University of Cape Town,
Rondebosch 7701, South Africa
Mathematics Department, Macquarie University, Sydney, NSW 2109, Australia