Generalized Canonical Isomorphisms on Determinant

In this paper we define tensor modules (sheaves) of Schur type and of generalized Schur type associated with given modules (sheaves), using the so-called Schur functors. According to the functorial property, we give a series of tensor modules (sheaves) of Schur types in a categorical description. The main conclusion is that, by using basic ideas of algebraic geometry, there exists a canonical isomorphism of different tensor modules (sheaves) of Schur types if the original sheaf is locally free, which is in fact a generalization of results in linear algebra into locally free sheaves.