Completeness and Cocompleteness of R Smod 1N

Helmut Röhrl

A chapter in Papers in Honour of Bernhard Banaschewski, 2000, pp 257-269 from Springer

Abstract: Abstract In this paper we formalize the concept of absolutely convergent infinite series by introducing the notion of prenormed R-semimodule with N-summation, where N is an arbitrary class. The morphisms between such semimodules are the contractive homomorphisms of R-semimodules that ‘preserve’ N-summation. The category R Smod 1N of all prenormed R-semimodules with N-summation and their morphisms (composition being the set-theoretical one) fails to be an algebraic category. However, under quite general conditions it is both complete and cocomplete.

Keywords: prenormed semimodule; N-summation; complete; cocomplete; free objects.; Primary: 16Y60; Secondary: 18A99 (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-2529-3_14

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DOI: 10.1007/978-94-017-2529-3_14

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