Timeline for Definition of dense functors

7 events

when toggle format	what		by	license	comment
Jul 30, 2022 at 14:14	comment	added	Buschi Sergio		the comma category is natural in the top object, a particulate diagram no, Ind-categories theory is a way to have a surrogate of naturality for particular diagrams.
Dec 13, 2020 at 11:32	comment	added	Jochen Wengenroth		Very late to the party. If you would like to have something analogue to the density of the image of a function $f:C\to D$ (so that continuous functions $g$ on $D$ are determined by their compositions $g\circ f$) the notion of initial functors comes close: $F:C\to D$ is initial if and only, for every set-valued functor $G:D\to Set$, $G$ and $G\circ E$ have the same limit. You can characterize this by the fact that the comma category $(F/d)$ is non-empty and connected for every $d\in D$. Unfortunately, the nLab entries for dense and initial functors don't mention any relations.
Jun 14, 2016 at 12:51	vote	accept	Arrow
Jun 12, 2016 at 20:36	comment	added	Zhen Lin		In my view, the morally correct definition is that a dense functor is one such that the induced Yoneda representation is fully faithful. It is a consequence of the fact that every presheaf is a colimit of a canonical diagram that we obtain the equivalent characterisation in terms of colimits.
Jun 12, 2016 at 19:46	answer	added	Qiaochu Yuan		timeline score: 6
Jun 12, 2016 at 12:35	history	edited	Arrow	CC BY-SA 3.0	added 323 characters in body
Jun 12, 2016 at 12:10	history	asked	Arrow	CC BY-SA 3.0