  Dense or glassy active matter, as a result of its remarkable resemblance to
passive glass-forming materials, is enjoying increasing scientific interest. To
better grasp the subtle effect of active motion on the process of
vitrification, a number of active mode-coupling theories (MCTs) have recently
been developed. These have proven capable of qualitatively predicting important
parts of the active glassy phenomenology. However, most efforts so far have
only considered single-component materials, and their derivations are arguably
more complex than the standard MCT case, which might hinder broader usage. Here
we present a detailed derivation of a distinct active MCT for mixtures of
athermal self-propelled particles that is more transparent than previously
introduced versions. The key insight is that we can follow a similar strategy
for our overdamped active system as is typically used for passive underdamped
MCT. Interestingly, when only considering one particle species, our theory
gives the exact same result as the one obtained in previous work which employed
a highly different mode-coupling strategy. Moreover, we assess the quality of
the theory and its novel extension to multi-component materials by using it to
predict the dynamics of a Kob-Andersen mixture of athermal active Brownian
quasi-hard spheres. We demonstrate that our theory is able to capture all
qualitative features, most notably the location of the optimum of the dynamics
when the persistence length and cage length coincide, for each combination of
particle types.
