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Le vendredi 25 Novembre 2005 04:56, duraid@octopus.com.au a =E9crit :
> > Is there an accepted terminology for semigroups with many objects, i.=
e.
> > gadgets that satisfy the all the axioms satisfied by categories excep=
ting
> > those
> > which refer to identities ?
>
> Koslowski calls these "taxonomies", see e.g. "Monads and interpolads in
> bicategories" (TAC vol 3, no 8 (1997)).
>
>      Duraid

Dear all,

I call a "small semigroup with many objects enriched over the model categ=
ory=20
of compactly generated topological spaces" a "flow" in my work (these obj=
ects=20
are interesting for me only if they are enriched over very particular mod=
el=20
categories satisfying particular properties). The terminology comes from =
the=20
fact that I use them to study the time flow of a higher dimensional autom=
aton=20
(up to directed homotopy).=20

For "taxonomy", I would be very curious to know the origin of the termino=
logy.=20
What does it mean exactly ?

In the paper q-alg/9608025 "Flexible sheaves", Carlos Simpson calls a "(n=
ot=20
necessarily small) semigroup with many objects enriched over the category=
 of=20
topological spaces" a continuous semicategory.=20

I had also seen the word "precategory" but I cannot remember where. Bewar=
e of=20
the fact that the word precategory is also used for categories *with=20
identities* such that the composition law is partially defined : that is =
the=20
fact that the codomain of F is equal to the domain of G is not sufficient=
 for=20
GoF to exist. Once again, I cannot remember where I read this word. The o=
nly=20
thing I remember is that that was a computer-scientific work.

The word "non-unital category" is also used sometime in mathematical pape=
rs.=20

pg.