For natural numbers $r\ge 2$ and $n$ a complete classification of natural transformations $A:TT^{(r)}\rightarrow TT^{(r)}$ over $n$-manifolds is given, where $T^{(r)}$ is the linear $r$-tangent bundle functor.
@article{107719,
author = {W\l odzimierz M. Mikulski},
title = {The natural transformations $TT^{(r)}\to TT^{(r)}$},
journal = {Archivum Mathematicum},
volume = {036},
year = {2000},
pages = {71-75},
zbl = {1049.58009},
mrnumber = {1751615},
language = {en},
url = {http://dml.mathdoc.fr/item/107719}
}
Mikulski, Włodzimierz M. The natural transformations $TT^{(r)}\to TT^{(r)}$. Archivum Mathematicum, Tome 036 (2000) pp. 71-75. http://gdmltest.u-ga.fr/item/107719/
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