Product preserving gauge bundle functors on all principal bundle homomorphisms

Włodzimierz M. Mikulski. "Product preserving gauge bundle functors on all principal bundle homomorphisms." Annales Polonici Mathematici 101.2 (2011): 163-207. <http://eudml.org/doc/280410>.

@article{WłodzimierzM2011,
abstract = {Let 𝓟𝓑 be the category of principal bundles and principal bundle homomorphisms. We describe completely the product preserving gauge bundle functors (ppgb-functors) on 𝓟𝓑 and their natural transformations in terms of the so-called admissible triples and their morphisms. Then we deduce that any ppgb-functor on 𝓟𝓑 admits a prolongation of principal connections to general ones. We also prove a "reduction" theorem for prolongations of principal connections into principal ones by means of Weil functors. We observe that there exist plenty of such prolongations. In Appendix, we classify the natural operators lifting vector-valued 1-forms (or vector-valued maps) to vector-valued 1-forms on Weil bundles.},
author = {Włodzimierz M. Mikulski},
journal = {Annales Polonici Mathematici},
keywords = {natural bundles; gauge bundles; product preserving bundle functors; natural transformations; principal bundles; general connections; principal connections; Weil bundles; Weil algebras},
language = {eng},
number = {2},
pages = {163-207},
title = {Product preserving gauge bundle functors on all principal bundle homomorphisms},
url = {http://eudml.org/doc/280410},
volume = {101},
year = {2011},
}

TY - JOUR
AU - Włodzimierz M. Mikulski
TI - Product preserving gauge bundle functors on all principal bundle homomorphisms
JO - Annales Polonici Mathematici
PY - 2011
VL - 101
IS - 2
SP - 163
EP - 207
AB - Let 𝓟𝓑 be the category of principal bundles and principal bundle homomorphisms. We describe completely the product preserving gauge bundle functors (ppgb-functors) on 𝓟𝓑 and their natural transformations in terms of the so-called admissible triples and their morphisms. Then we deduce that any ppgb-functor on 𝓟𝓑 admits a prolongation of principal connections to general ones. We also prove a "reduction" theorem for prolongations of principal connections into principal ones by means of Weil functors. We observe that there exist plenty of such prolongations. In Appendix, we classify the natural operators lifting vector-valued 1-forms (or vector-valued maps) to vector-valued 1-forms on Weil bundles.
LA - eng
KW - natural bundles; gauge bundles; product preserving bundle functors; natural transformations; principal bundles; general connections; principal connections; Weil bundles; Weil algebras
UR - http://eudml.org/doc/280410
ER -