Geodesic
On principal connection like bundles
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 4, pp. 961-967
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Let $\mathcal {P}\mathcal {B}_m$ 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 $\mathcal {P}\mathcal {B}_m$ of order $r$ by means of the $(r,m)$-systems. Next we present several interesting examples of fiber product preserving gauge bundle functors on $\mathcal {P}\mathcal {B}_m$ of order $r$. Finally, we introduce the concept of product preserving $(r,m)$-systems and describe all fiber product preserving gauge bundle functors on $\mathcal {P}\mathcal {B}_m$ of order $r$ by means of the product preserving $(r,m)$-systems.
Let $\mathcal {P}\mathcal {B}_m$ 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 $\mathcal {P}\mathcal {B}_m$ of order $r$ by means of the $(r,m)$-systems. Next we present several interesting examples of fiber product preserving gauge bundle functors on $\mathcal {P}\mathcal {B}_m$ of order $r$. Finally, we introduce the concept of product preserving $(r,m)$-systems and describe all fiber product preserving gauge bundle functors on $\mathcal {P}\mathcal {B}_m$ of order $r$ by means of the product preserving $(r,m)$-systems.
DOI : 10.1007/s10587-014-0146-1
Classification : 58A05, 58A20, 58A32
Keywords: principal bundle; principal connection; gauge bundle functor; natural transformation 
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     title = {On principal connection like bundles},
     journal = {Czechoslovak Mathematical Journal},
     pages = {961--967},
     year = {2014},
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Mikulski, Włodzimierz M. On principal connection like bundles. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 4, pp. 961-967. doi: 10.1007/s10587-014-0146-1

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