natural operator; tensor field; natural functional; Lie derivative
This short note completes the results of  by removing the locality assumption on the operators. After providing a quick survey on (infinitesimally) natural operations, we show that all the bilinear operators classified in  can be characterized in a completely algebraic way, even without any continuity assumption on the operations.
 Čap, Andreas, Slovák, Jan: On multilinear operators commuting with Lie derivatives
. Ann. Global Anal. Geom. 13 (3) (1995), 251–279. DOI 10.1007/BF00773659
| MR 1344482
 Kolář, Ivan, Michor, Peter W., Slovák, Jan: Natural operations in Differential Geometry
. Springer, 1993, vi+434 pp. MR 1202431