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arXiv · 2206.00949

A symmetric approach to higher coverings in categorical Galois theory

Fara Renaud·Tim Van der Linden
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Abstract

In the context of a tower of (strongly Birkhoff) Galois structures in the sense of categorical Galois theory, we show that the concept of a higher covering admits a characterisation which is at the same time absolute (with respect to the base level in the tower), rather than inductively defined relative to extensions of a lower order; and symmetric, rather than depending on a perspective in terms of arrows pointing in a certain chosen direction. This result applies to the Galois theory of quandles, for instance, where it helps us characterising the higher coverings in purely algebraic terms.

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Fara Renaud, Tim Van der Linden. 2022-06-02. A symmetric approach to higher coverings in categorical Galois theory. https://doi.org/10.1007/s10485-022-09698-6

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