#colimit — Public Fediverse posts
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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.
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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.