  We give a new proof of homological stability with the best known isomorphism
range for mapping class groups of surfaces with respect to genus. The proof
uses the framework of Randal-Williams-Wahl and Krannich applied to disk
stabilization in the category of bidecorated surfaces, using the Euler
characteristic instead of the genus as a grading. The monoidal category of
bidecorated surfaces does not admit a braiding, distinguishing it from
previously known settings for homological stability. Nevertheless, we find that
it admits a suitable Yang-Baxter element, which we show is sufficient structure
for homological stability arguments.
