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Entwined modules over linear categories and Galois extensions

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Abstract

In this paper, we study modules over quotient spaces of certain categorified fiber bundles. These are understood as modules over entwining structures involving a small K-linear category \({\cal D}\) and a K-coalgebra C. We obtain Frobenius and separability conditions for functors on entwined modules. We also introduce the notion of a C-Galois extension \({\cal E} \subseteq {\cal D}\) of categories. Under suitable conditions, we show that entwined modules over a C-Galois extension may be described as modules over the subcategory \({\cal E}\) of C-coinvariants of \({\cal D}\).

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India

    Mamta Balodi, Abhishek Banerjee & Samarpita Ray

Authors
  1. Mamta Balodi
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  2. Abhishek Banerjee
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  3. Samarpita Ray
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Corresponding author

Correspondence to Abhishek Banerjee.

Additional information

M.B. was also supported by SERB NPDF grant PDF/2017/000229.

A.B. was also supported by SERB Matrics fellowship MTR/2017/000112.

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Balodi, M., Banerjee, A. & Ray, S. Entwined modules over linear categories and Galois extensions. Isr. J. Math. 241, 623–692 (2021). https://doi.org/10.1007/s11856-021-2108-2

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  • DOI: https://doi.org/10.1007/s11856-021-2108-2

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