Reduction of exact structures (Q2332154)

For an additive category \(\mathscr{A}\), the authors study the complete lattice \(\mathrm{Ex}(\mathscr{A})\) of exact structures. An alternative but more general approach to matrix reduction techniques of the Kiev school is suggested by keeping the objects and reducing the exact structure, so that in a finitary situation, the split exact structure is reached as the ultimate reduction. Results on the Gabriel-Roiter measure are generalized to exact categories and studied with respect to changement of exact structures.