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Galois extensions of braided tensor categories and braided crossed G-categories

· 2002 · math.CT · arXiv math/0209093

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abstract

We show that the author's notion of Galois extensions of braided tensor categories [22], see also [3], gives rise to braided crossed G-categories, recently introduced for the purposes of 3-manifold topology [31]. The Galois extensions C \rtimes S are studied in detail, and we determine for which g in G non-trivial objects of grade g exist in C \rtimes S.

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Generalised Orbifolds and G-equivariantisation

math.QA · 2025-06-09 · accept · novelty 6.0

Generalised orbifold categories of G-crossed ribbon categories are ribbon equivalent to G-equivariantisations, via an explicit functor.

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  • Generalised Orbifolds and G-equivariantisation math.QA · 2025-06-09 · accept · none · ref 16 · internal anchor

    Generalised orbifold categories of G-crossed ribbon categories are ribbon equivalent to G-equivariantisations, via an explicit functor.