0 A Working Language of Compositionality

LINCS begins from a simple observation: a learning system is assembled from parts, and the ways those parts are composed carry meaning. An encoder feeds a predictor; an intervention changes a state; local models exchange information on overlaps; argument roles connect evidence to a claim. Category theory provides a language for saying which compositions are possible and which compositions are intended to agree.

This chapter develops the portion of that language used throughout the book. It is not a miniature survey of category theory. Its purpose is practical: after reading it, one should be able to identify the objects and arrows in a LINCS application, read its diagrams, understand what its sketch declares, and distinguish a structural obstruction from a numerical measurement of that obstruction.

¹1. The central reading habit is type first. Before asking for a formula or a loss, ask for the source and target of every map and for the two routes that are being compared. ↩