Nucleus I: Adjunction spectra in recommender systems and descent. (arXiv:2004.07353v4 [math.CT] UPDATED)

Recommender systems build user profiles using concept analysis of usage
matrices. The concepts are mined as spectra and form Galois connections.
Descent is a general method for spectral decomposition in algebraic geometry
and topology which also leads to generalized Galois connections. Both
recommender systems and descent theory are vast research areas, separated by a
technical gap so large that trying to establish a link would seem foolish. Yet
a formal link emerged, all on its own, bottom-up, against authors’ intentions
and better judgment. Familiar problems of data analysis led to a novel solution
in category theory. The present paper arose from a series of earlier efforts to
provide a top-down account of these developments.