Infinitary addition, real numbers, and taut monads

George Janelidze*, Ross Street

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review


    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.

    Original languageEnglish
    Pages (from-to)1047-1064
    Number of pages18
    JournalApplied Categorical Structures
    Issue number5
    Early online date18 Apr 2018
    Publication statusPublished - Oct 2018

    Bibliographical note

    A correction to this article exists and has been incorporated into the original. It can be found at doi: 10.1007/s10485-018-9528-0


    • Cardinal algebra
    • Commutative monoid
    • Infinitary addition
    • Lextensive category
    • Monoidal category
    • Positive reals
    • Series monoid
    • Summation
    • Taut monad


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