#functor — Public Fediverse posts

C++OnSea 2025 SESSION ANNOUNCEMENT: Safe and Readable Code: Monadic Operations in C++23 by @asperamanca

https://cpponsea.uk/2025/session/safe-and-readable-code-monadic-operations-in-cpp23

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#expected #functor #monad #optional #ranges

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).

@nuttycom @me If we agree that "map" is a good name for what "fmap" does (and as a non-native speaker of English, I think it is), then the adjectival-ish name of Functor could simply be "Mappable".

#fmap #Functor #namingThings

Recall that a #colimit of a #diagram in a #category C, that is, of a #functor F:J→C, is #given by a #universal [[#cocone]] for F. A [[#co #cone]] for F is a #natural #transformation from F to a #constant diagram,

Δ(c)=(J→1→cC),

so that a cocone for F is an #object of a #comma category,

F↓Δ,

where Δ:C1→CJ is the #diagonal functor #obtained by #pulling #back #along the #unique functor J→1. A universal cocone is #simply an #initial object of F↓Δ.

Recall that a #colimit of a #diagram in a #category C, that is, of a #functor F:J→C, is #given by a #universal [[#cocone]] for F. A [[#co #cone]] for F is a #natural #transformation from F to a #constant diagram,

Δ(c)=(J→1→cC),

so that a cocone for F is an #object of a #comma category,

F↓Δ,

where Δ:C1→CJ is the #diagonal functor #obtained by #pulling #back #along the #unique functor J→1. A universal cocone is #simply an #initial object of F↓Δ.