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Parallel Transport on a Lie 2-Group Bundle over a Lie Groupoid Along Haefliger Paths

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Abstract

Incorporating the cartesian morphism lifting property from the theory of fibered categories with the horizontal path lifting property of differential geometric connection structures, we develop a theory of parallel transport on principal Lie 2-group bundles over Lie groupoids along certain class of Haefliger paths on base Lie groupoids. We establish thin homotopy invariance and extend our theory to the framework of VB-groupoids through associated bundle construction. Throughout the paper, our results are rooted in the Grothendieck’s correspondence between fibered categories and pseudofunctors.

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Notes

  1. We took help of the Chatgpt to find a specific example of a group satisfying the conditions.

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Acknowledgements

Chaudhuri acknowledges the support of SRF-fellowship provided by IISER-TVM; much of his work on this paper was done during his stay at the Indian Institute of Science Education and Research Thiruvananthapuram, IISER-TVM. Authors sincerely thank the anonymous referee for the extensive comments and valuable suggestions, which have led to significant improvements in the article.

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  1. School of Mathematics, Indian Institute of Science Education and Research Thiruvananthapuram, Maruthamala P.O., Vithura, Kerala, 695551, India

    Saikat Chatterjee

  2. Machine Intelligence Unit, Indian Statistical Institute, Kolkata, 700108, India

    Adittya Chaudhuri

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  1. Saikat Chatterjee
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  2. Adittya Chaudhuri
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Chatterjee, S., Chaudhuri, A. Parallel Transport on a Lie 2-Group Bundle over a Lie Groupoid Along Haefliger Paths. Appl Categor Struct 34, 62 (2026). https://doi.org/10.1007/s10485-026-09897-5

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