We introduce the concept of modified vertical Weil functors on the category $mathcal{F}mathcal{M}_m$ of fibred manifolds with $m$-dimensional bases and their fibred maps with embeddings as base maps. Then we describe all fiber product preserving bundle functors on $mathcal{F}mathcal{M}_m$ in terms of modified vertical Weil functors. The construction of modified vertical Weil functors is an (almost direct) generalization of the usual vertical Weil functor. Namely, in the construction of the usual vertical Weil functors, we replace the usual Weil functors $T^A$ corresponding to Weil algebras $A$ by the so called modified Weil functors $T^A$ corresponding to Weil algebra bundle functors $A$ on the category $mathcal{M}_m$ of $m$-dimensional manifolds and their embeddings.
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机译：我们在$ mathcal {F} mathcal {M} _m $类具有$ m $维基数的纤维歧管及其带嵌入图的纤维图作为基础图的基础上，介绍了改进的垂直Weil函子的概念。然后，我们根据修改后的垂直Weil函子描述$ mathcal {F} mathcal {M} _m $上所有保留光纤产品的束函数。改良的垂直Weil函子的构造是对常规垂直Weil函子的（几乎直接）概括。即，在构造通常的竖向Weil函子时，我们用对应于Weil代数束函子$ A的所谓的改进的Weil函子$ T ^ A $来代替对应于Weil代数$ A $的通常Weil函子$ T ^ A $。 $ m $维流形及其嵌入的$ mathcal {M} _m $类别中的$。
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