On some concepts in the theory of Lie algebroids (Q6606771)

Lie algebroids arise as reductions of the tangent bundle to a Lie groupoid. Namely, given a Lie groupoid \(G \rightrightarrows M\), the Lie algebroid \(A(G)\) of \(G\) is the vector bundle whose sections are right invariant (source vertical) vector fields on \(G\). Tangent bundles and Lie algebras are standard instances of Lie algebroids. The author answers the following question:\N\NWhat if, in the above setting, we replace tangent bundles with \textit{higher tangent bundles} (i.e. higher jets of curves at \(0\))?\N\NIn other words, what is the algebraic structure encoding the reduction of higher tangent bundles of Lie groupoids? The author's answer uses the notion of vector bundle comorphism. Higher tangent bundles and higher tangent spaces to Lie groups at the unit are standard instances of the higher Lie algebroids defined by the author in this way.\N\NFor the entire collection see [Zbl 1531.53004].