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05 November 2024
 
  » arxiv » 2206.00949

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A symmetric approach to higher coverings in categorical Galois theory
Fara Renaud ; Tim Van der Linden ;
Date 2 Jun 2022
AbstractIn 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.
Source arXiv, 2206.00949
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