Homotopy Type Theory divisible group > history (Rev #6)


An abelian group GG is a divisible group if there exists a multiplicative +\mathbb{Z}_{+}-action α: +(GG)\alpha:\mathbb{Z}_{+} \to (G \to G), where +\mathbb{Z}_{+} is the positive integers, such that for all n: +n:\mathbb{Z}_{+} and all g:Gg:G, the fiber of α(n)\alpha(n) at gg is contractible:

n: + g:GisContr(fiber(α(n),g))\prod_{n:\mathbb{Z}_{+}} \prod_{g:G} \mathrm{isContr}(\mathrm{fiber}(\alpha(n),g))

See also


  • Phillip A. Griffith (1970), Infinite Abelian group theory. Chicago Lectures in Mathematics. University of Chicago Press. ISBN 0-226-30870-7

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