NATURAL TRANSFORMATIONS OF SEPARATED JETS

Miroslav Doupovec and Ivan Kolár

Address. Miroslav Doupovec, Department of Mathematics, FSI VUT Brno, Technicka 2, 616 69 Brno, Czech Republic

Ivan Kolar, Department of Algebra and Geometry, Masaryk University, Janackovo nam. 2a, 662 95 Brno, Czech Republic

E-mail: doupovec@mat.fme.vutbr.cz, kolar@math.muni.cz

Abstract. Given a map of a product of two manifolds into a third one, one can define its jets of separated orders $r$ and $s$. We study the functor $J^{r;s}$ of separated $(r;s)$-jets. We determine all natural transformations of $J^{r;s}$ into itself and we characterize the canonical exchange $J^{r;s}\to J^{s;r}$ from the naturality point of view.

AMSclassification. 58A2

Keywords. Separated jet, canonical exchange, natural transformation