Fusion rules for pastures and tracts

Baker and Bowler defined a category of algebraic objects called tracts which generalize both partial fields hyperfields. They also notion weak strong matroids over tract F , proved that if is perfect, meaning -vectors -covectors are orthogonal for every matroid then the notions -matroids coincide. We define class strongly fused prove such perfect. show stringent hyperfields fused; in this way, our criterion perfection generalizes results Baker–Bowler Bowler–Pendavingh.