categories: (lluf)+(2==>3)=?

[jean benabou <jean.benabou@wanadoo.fr>]

There have been many mails about lluf subcategories X' of a category X.

In many meaningful cases such subcategories satisfy the following extra
property:

(2==>3)   If two maps of a commutative triangle of X belong to X' so does
the third.

Examples of such X's are : the maps f of X which are inverted by a functor
F:X-->Y, or those such that F(f) is an identity, i.e. the "vertical" maps.
If X is a groupoid a  subcategry X' of X need not be a subgroupoid. It is
iff it satisfies (2==> 3).

I would like to know if the property  (lluf)+(2==>3) , which has certainly
been met by many people, has a name. (It certainly deserves to be named). In
case it does not have one, I am tempted by:

       "X' is a strip of X",   or even better:   "X' is a wide strip of X"

The second name would permit to use "strip" for (2==>3) and "wide", a la
Ronnie Brown, for lluf. It is easy to translate, e.g. in French by "large
bande", and to me it seems descriptive and flexible. But of course English
is not my mother tongue, and I am open to all suggestions.

Thanks, and, a bit late, a happy New Year to all..