Simple Situation

Simple Situation

[Ellis D. Cooper]

Dear categorists,

Let C be a category with a distinguished sub-category E and a
distinguished family S of morphisms
such that for every object x of C there is a unique morphism f_x: x
---> e_x with e_x an object of E
so that the following conditions are satisfied: (1) if x is in E then
f_x = 1_x (the identity morphism
of x), (2) if s: x ---> y is in S then e_y = e_x and f_x = f_y s.

Hasn't this simple situation been named and incorporated in some
publication on category
theory? A reference would be most appreciated.

Ellis D. Cooper



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Simple Situation

[Prof. Peter Johnstone]

If I've understood it right, this is exactly the concept of a
"multi-terminal object" (that is, a multi-limit for the empty
diagram). The name is due to me (in a paper called "A syntactic
approach to Diers's localizable categories" in SLNM 753 (1979)),
but the concept is due to Yves Diers: see his "Familles
universelles de morphismes", Ann. Soc. Sci. Bruxelles 93 (1979).

Peter Johnstone

On Fri, 4 Dec 2009, Ellis D. Cooper wrote:

> Dear categorists,
>
> Let C be a category with a distinguished sub-category E and a
> distinguished family S of morphisms
> such that for every object x of C there is a unique morphism f_x: x
> ---> e_x with e_x an object of E
> so that the following conditions are satisfied: (1) if x is in E then
> f_x = 1_x (the identity morphism
> of x), (2) if s: x ---> y is in S then e_y = e_x and f_x = f_y s.
>
> Hasn't this simple situation been named and incorporated in some
> publication on category
> theory? A reference would be most appreciated.
>
> Ellis D. Cooper
>

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]