Functoriality and uniformity in Hrushovski's groupoid-cover correspondence. (arXiv:1711.03531v1 [math.LO])

The correspondence between definable connected groupoids in a theory \$T\$ and internal generalised imaginary sorts of \$T\$, established by Hrushovski in ["Groupoids, imaginaries and internal covers," Turkish Journal of Mathematics, 2012], is here extended in two ways: First, it is shown that the correspondence is in fact an equivalence of categories, with respect to appropriate notions of morphism. Secondly, the equivalence of categories is shown to vary uniformly in definable families, with respect to an appropriate relativisation of these categories. Some elaboration on Hrushovki's original constructions are also included.查看全文

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 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 The correspondence between definable connected groupoids in a theory \$T\$ and internal generalised imaginary sorts of \$T\$, established by Hrushovski in ["Groupoids, imaginaries and internal covers," Turkish Journal of Mathematics, 2012], is here extended in two ways: First, it is shown that the correspondence is in fact an equivalence of categories, with respect to appropriate notions of morphism. Secondly, the equivalence of categories is shown to vary uniformly in definable families, with respect to an appropriate relativisation of these categories. Some elaboration on Hrushovki's original constructions are also included.