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From: Pierre Cardascia
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Subject: A theorem from Herrlich and Strecker
Date: Wed, 15 Apr 2009 19:35:34 +0000 (GMT)
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Dear Cat=E9goristes,=0A=0AI'm working on an introduction for categorical lo=
gic, and I try to avoid using the notion of limit before introducing the no=
tion of functor in my work (because limit means limit of functors. Squarely=
, we can introduce the limit before, but we don't understand why the limit =
is called limit, and limit of what ??).=0ABut I have to introduce the notio=
n of categories finitely complete. SO I think about this theorem :=0A=3D=3D=
=3D> If C has a terminal object, and a pullback for each pair of arrows wit=
h common codomains, then C is finitively complete.=0AI found that without a=
ny proof in Goldblatt. Rob Goldblatt just said : "you can find it into such=
book from Herrlich and Strecker"... Does somebody has the proof ? Can I us=
e this theorem to define complety closed categories instead of working with=
limits ? Or does somebody have any way to define complety closed categorie=
s without any reference to functors ?=0A=0AThanks !=0A=0APierre CARDASCIA=
=0A=0A=0A