Abstract
Let PB m be the category of all principal fibred bundles with m-dimensional bases and their principal bundle homomorphisms covering embeddings. We introduce the concept of the so called (r,m)-systems and describe all gauge bundle functors on PB m of order r by means of the (r,m)-systems. Next we present several interesting examples of fiber product preserving gauge bundle functors on PB m of order r. Finally, we introduce the concept of product preserving (r,m)-systems and describe all fiber product preserving gauge bundle functors on PB m of order r by means of the product preserving (r,m)-systems.
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Mikulski, W.M. On principal connection like bundles. Czech Math J 64, 961–967 (2014). https://doi.org/10.1007/s10587-014-0146-1
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DOI: https://doi.org/10.1007/s10587-014-0146-1