Traditional generalized function theories (such as Schwartz's distribution theory and Colombeau algebra) have limitations in describing certain phenomena [1]. To address this issue, the Generalized Mapping theory is proposed, which realizes the mathematical modeling of dynamic behavior-result correlations through a four-element framework consisting of an object set A, an operation set F, a result set B, and a generative relation ⊢. However, when the Generalized Mapping theory was initially proposed, its two forms were formulated and defined using sets. Although set-based definitions can describe the basic logic of the theory, they are insufficient in practical applications, especially in computer simulations. Since vector, matrix, and even tensor computations are frequently required (despite sets being occasionally treatable as vectors), it is necessary to theoretically extend the Generalized Mapping theory to tensors. Additionally, there are scenarios where conversion between its two forms is needed. Therefore, this paper presents the tensor extension of the Generalized Mapping theory and discusses the theoretical conditions required for converting between its two forms.