Infinitary Addition, Real Numbers, and Taut Monads

Infinitary Addition, Real Numbers, and Taut Monads Appl Categor Struct https://doi.org/10.1007/s10485-018-9524-4 Infinitary Addition, Real Numbers, and Taut Monads 1 2 George Janelidze · 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 numbers. 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Categorical Structures Springer Journals

Infinitary Addition, Real Numbers, and Taut Monads

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Publisher
Springer Netherlands
Copyright
Copyright © 2018 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Mathematics; Mathematical Logic and Foundations; Theory of Computation; Convex and Discrete Geometry; Geometry
ISSN
0927-2852
eISSN
1572-9095
D.O.I.
10.1007/s10485-018-9524-4
Publisher site
See Article on Publisher Site

Abstract

Appl Categor Struct https://doi.org/10.1007/s10485-018-9524-4 Infinitary Addition, Real Numbers, and Taut Monads 1 2 George Janelidze · 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 numbers. 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

Journal

Applied Categorical StructuresSpringer Journals

Published: Apr 18, 2018

References

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