The constructions of general connections on the fibred product of q copies of the first jet prolongation

We describe all natural operators \(A\) transforming general connections \(\Gamma\) on fibred manifolds \(Y \rightarrow M\) and torsion-free classical linear connections \(\Lambda\) on \(M\) into general connections \(A(\Gamma,\Lambda)\) on the fibred product \(J^{&lt;q&gt;}Y \rightarrow M\) of \(q\) copies of the first jet prolongation \(J^{1}Y \rightarrow M\).<br /><br />

The fibred product near-rings and near-ring modules for certain categories

In somes categories, there are structures that look very much like groups, and they usually are. These structures are called group-objects and were first studied by Eckmann and Hilton (1). If our category has an object T such that hom(X, T)= {tx}, a singleton, for each object X ∈ Ob , T is called a terminal object. Our category must have products; i.e. for A1,…, An ∈;. Ob , there is an object A1 × … × An ∈ Ob and morphisms pi: A1 × … × An → Ai so that if fi: X → Ai, i = 1, 2, …, n, are morphisms of , then there is a unique morphism [f1, …, fn]: X → A1 × … × An such that for i = 1, 2, …, n.