Re: Reference requested

["jpradines" <jpradines@wanadoo.fr>]

The use of a lot of terminologies stemming from topology for describing 
purely algebraic properties seems to be widespread  and fashionable among  an 
important part of the community of categorists.
This may be a convenient source of intuition and analogies by giving a 
topological or geometrical fragrance to such algebraic concepts.
However the considerable drawback is that this habit is a source of 
unsolvable clashes for people who are currently using topological or more 
specially Lie groupoids, more generally structured (in Ehresmann's sense), 
i. e. internal, groupoids, who are obliged to create alternative 
terminologies.
For the special case of the duet discrete/undiscrete (or indiscrete, or 
sometimes coarse) I'm personally using presently null/banal (there are a lot 
of different terminologies used by various authors).
(As to the term "chaotic", I prefer to avoid comments, being afraid to 
perturb the beautifully non chaotic weather we are presently enjoying in our 
region).

Jean Pradines

----- Message d'origine ----- 
De : "Ronnie Brown" <ronnie.profbrown@btinternet.com>
À : "Peter May" <may@math.uchicago.edu>
Cc : <categories@mta.ca>
Envoyé : jeudi 29 septembre 2011 15:41
Objet : categories: Re: Reference requested


> Why not use the term `indiscrete groupoid' for the functor that gives a
> right adjoint to the  functor Ob: Groupoids \to Sets?   The left adjoint
> is then of course the `discrete groupoid'.  This agrees with the
> terminology for discrete and indiscrete topologies.
>
> I confess to have used different  terminology in various places.
>
> Of course one use of these notions is to show that the functor Ob
> preserves limits and colimits, which is  a start on constructing them.
>
> It is not surprising that this concept occurs widely. In groupoids there
> is a notion of covering morphism and the universal cover of a group G
> is of course an indiscrete groupoid G'; this groupoid is by no means
> `trivial' since it comes equipped with a covering morphism  p: G' \to
> G.  This approach to covering space theory is given in my book `Topology
> and groupoids'.
>
> Ronnie
>
>

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