I don't know anything about algebraic geometry or category theory or haskell, but I know some stuff about the normal boring kind of linear algebra, and in some places the author relies on statements like "since the eigenvalues are real and positive we can conclude that it is a symmetric positive definite matrix" which I know are just wrong (it wouldn't have to be symmetric). This is particularly bad because the rest of the argument (for example in 6.2.2) explains why it's so cool that we've shown it's symmetric (we haven't).