The GraphBLAS is a set of basic building blocks for constructing graph algorithms in terms of linear algebra. They are first and foremost defined mathematically with the goal that language bindings will be produced for a wide range of programming languages. We started with the C programming language and over the last four years have produced multiple versions of the GraphBLAS C API specification. In this paper, we describe our next version of the C GraphBLAS specification. It introduces a number of major changes including support for multithreading, import/export functionality, and functions that use the indices of matrix/vector elements. Since some of these changes introduce small backwards compatibility issues, this is a major release we call GraphBLAS 2.0.