Matrix properties are a particular type of exactness properties that can be seen as category-theoretic analogues of linear Mal'tsev conditions in Universal Algebra. See this list for relevant papers in this research area.
The study of matrix properties led to the theory of "approximate operations" developed jointly with Dominique Bourn, and a general theory of exactness properties developed jointly with Pierre-Alain Jacqmin.
Work in progress on matrix properties:
- Open problem on finding an algorithm for implication of basic matrix properties solved - see the working version of the preprint.
- Even for binary matrices, the preorder of implications is quite complex. Some new results on this appear in this work in progress.
- Python implementation of the algorithm for deducing implication of (basic) matrix properties can be found here. The program needs to be improved in some future.