#functor — Public Fediverse posts on home.social

Short #categorytheory lesson: There is a common figure of speech, that goes like "If x is like y, then z is like q", e.g. "If a school are like a corporation, then the teachers are like bosses". This figure of speech introduces a #functor: what are you saying is that there is a certain connection (or category-theory therms a "morphism") between schools and teachers, that is similar to the connection between corporations and bosses i.e. that there is some kind of structure preserving map that connects the category of school-related things, to the category of work-related things in which schools (a) are mapped to corporations (F a) and teacher (b) are mapped to bosses (F b). and the connections between schools and teachers (a -> b) are mapped to the connections between corporations and bosses (F a -> F b).