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We construct and establish results for a categorical counterpart of pushforwards of connections on principal bundles. This categorical pushforward takes as input a categorical connection A_P on a categorical bundle P and an appropriate functor S: P -> Q and outputs a categorical connection S_*A_P on the categorical bundle Q. Applying this construction to the case of categorical bundles arising from decorated path spaces in principal bundles, we obtain a transformation of classical connections that combines the traditional gauge transformation with an affine translation.
@article{TAC_2022_38_a24,
author = {Saikat Chatterjee and Amitabha Lahiri and Ambar N. Sengupta},
title = {Pushforwards and {Gauge} {Transformations} for {Categorical} {Connections}},
journal = {Theory and applications of categories},
pages = {1015--1049},
publisher = {mathdoc},
volume = {38},
year = {2022},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TAC_2022_38_a24/}
}
TY - JOUR AU - Saikat Chatterjee AU - Amitabha Lahiri AU - Ambar N. Sengupta TI - Pushforwards and Gauge Transformations for Categorical Connections JO - Theory and applications of categories PY - 2022 SP - 1015 EP - 1049 VL - 38 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TAC_2022_38_a24/ LA - en ID - TAC_2022_38_a24 ER -
%0 Journal Article %A Saikat Chatterjee %A Amitabha Lahiri %A Ambar N. Sengupta %T Pushforwards and Gauge Transformations for Categorical Connections %J Theory and applications of categories %D 2022 %P 1015-1049 %V 38 %I mathdoc %U http://geodesic.mathdoc.fr/item/TAC_2022_38_a24/ %G en %F TAC_2022_38_a24
Saikat Chatterjee; Amitabha Lahiri; Ambar N. Sengupta. Pushforwards and Gauge Transformations for Categorical Connections. Theory and applications of categories, Tome 38 (2022), pp. 1015-1049. http://geodesic.mathdoc.fr/item/TAC_2022_38_a24/