Abstract
We extend the concept of vertical Weil functors VA corresponding to Weil algebras A to the one of generalized vertical Weil functors VA on FMm corresponding to Weil algebra bundle functors A on Mfm. Next, we show that the fiber product preserving bundle functors F on FMm of vertical type are the generalized vertical Weil functors VA on FMm. That F is of vertical type it means that Fxf:FxY→FxY1 depends only on fx:Yx→Yx1 for any FMm objects Y and Y1 with the same base and any FMm-map f:Y→Y1 with the identity as the base map.
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