Categorical constructions on heaps and modules over trusses are considered and contrasted with the corresponding constructions on groups and rings. These include explicit description of free heaps and free Abelian heaps, coproducts or direct sums of Abelian heaps and modules over trusses, and description and analysis of free modules over trusses. It is shown that the direct sum of two non-empty Abelian heaps is always infinite and isomorphic to the heap associated to the direct sum of the group retracts of both heaps and \(\mathbb {Z}\). Direct sum is used to extend a given truss to a ring-type truss or a unital truss (or both). Free modules are constructed as direct sums of a truss with itself. It is shown that only free rank-one module over a ring are free as modules over the associated truss. On the other hand, if a (finitely generated) module over a truss associated to a ring is free, then so is the corresponding quotient-by-absorbers module over this ring.

考虑了桁架上的堆和模块的分类构造，并将其与组和环上的相应构造进行对比。其中包括对自由堆和自由Abelian堆，桁架上的Abelian堆和模块的副产品或直接总和的明确描述，以及对桁架上的自由模块的描述和分析。结果表明，两个非空的Abelian堆的直接总和总是与与两个堆和\（\ mathbb {Z} \）的组缩回的直接总和相关联的堆同构。。直接求和用于将给定的桁架扩展为环形桁架或单元桁架（或两者）。自由模块被构造为其自身的桁架的直接总和。结果表明，只有环上的自由秩一模块作为相关桁架上的模块是自由的。另一方面，如果与一个环相关联的桁架上的（有限生成的）模块是自由的，则该环上的相应的吸收体商模块也将是自由的。