  Recently, M.~Baker and N.~Bowler introduced the notion of matroids over
hyperfields as a unifying theory of various generalizations of matroids. In
this paper we generalize the notion of minors and direct sums from ordinary
matroids to matroids over hyperfields. Using this we generalize the classical
construction of matroid-minor Hopf algebras to the case of matroids over
hyperfields.
