Group Completions Ⅰ : An Observation from a Category-Theoretical Point of View on the Ordinary Group Completions of Commutative Monoids

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  • Group Completions 1 : An Observation from a Category-Theoretical Point of View on the Ordinary Group Completions of Commutative Monoids

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Abstract

type:Departmental Bulletin Paper

In　this　series　on　group　completions　various　categorical　constructions　of　universal　grouplike　objects　from　symmetric　monoidal　objects　will　be　studied.　This　paper　is　the　first　part in　which　we　deal　with　the　ordinary　group　completions　of　commutative　monoids　and　observe some　other　aspects　than　the　ordinary　Grothendieck　group　construction.　The　relations　of the　ordinary　construction　with　colimits　and　lax　colimits　over　the　translation　category　of　a commutative　monoid　are　established.　Further　we　consider the　commutativity　of　the　group completion　construction　with　limits　and　lax　limits　over　a　group(i.e.　Galois　descent).

identifier:滋賀大学教育学部紀要, 3, 自然科学, 第48号, pp.67-74

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