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NATURAL TRANSFORMATIONS OF SEPARATED JETS

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*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