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Let $Y\to M$ be a fibered manifold over a manifold $M$ and $\mu: A\to B$ be a homomorphism between Weil algebras $A$ and $B$. Using the results of Mikulski and others, which classify product preserving bundle functors on the category of fibered manifolds, the author classifies all natural operators $T_{\text {proj}} Y\to T^\mu Y$, where $T_{\text {proj}}Y$ denotes the space of projective vector fields on $Y$ and $T^\mu$ the bundle functors associated with $\mu$.
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