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arXiv · 2606.12482

Categorical Hopf map

Ali Khalili Samani
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Abstract

We introduce the categorical Hopf map as a categorical principal bundle over the two-dimensional sphere with fibre the categorical circle of Nora Ganter. We investigate its connection to the Hopf map. We present a factorisation of the categorical Hopf map through the Hopf map and the basic bundle gerbe over the three-dimensional sphere. We discuss three equivalent constructions for the basic bundle gerbe over the three-dimensional sphere. Finally, we conjecture that the categorical group String(3) is equivalent to the categorical group of symmetries of the categorical Hopf map.

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Ali Khalili Samani. 2026-06-10. Categorical Hopf map. https://arxiv.org/abs/2606.12482

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