Subject: Topos
Date: Fri, 25 Oct 2002 14:21:00 -0500 (CDT)
From: "Carlos Prieto (113)"
To: Don Davis
Dear Don, I resend my previous message because a line was missing.
I refer to the question of Jianzhong Pan about the origin and meaning of
the word "topos". I asked a colleague at my Institute, Francisco
Marmolejo, who is an expert in category theory and he helped me to
remember what I once learned some years ago.
I remember hearing the word for the first time in the late seventies in a
series of lectures 'on topoi as foundation for the theories of sets
and sheaves', given by S. Mac Lane in Heidelberg. It appears that the
word was already used by Artin, Grothendieck, Verdier (in the
so-called SGA4). There they speak about what today is called Grothendieck
topos, and it was probably Grothendieck who first used the name. Nowadays,
topos refers to something more general. The word comes probably from
'topology' in the sense that after considering sheaves over 'topological'
spaces, in the generalizations that he wanted to do, that was not enough,
and so he generalized the idea of coverings of a topological space to
families of arrows with the same codomain in a given category. These
sheaf categories are what in SGA4 are called 'topoi'.
I hope this helps our colleague.
Sincerely,
Carlos Prieto
--
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PROF. CARLOS PRIETO
Instituto de Matemáticas, UNAM
04510 México, DF, MÉXICO
cprieto@math.unam.mx
Tel. (++52-55) 5622-4489,-4520
Fax (++52-55) 5616 0348
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Saludos
Q