From: Philippe Gaucher <gaucher@pps.jussieu.fr>
To: categories@mta.ca
Subject: Bibliographical reference needed
Date: Tue, 14 Feb 2006 12:52:32 +0100 [thread overview]
Message-ID: <E1F9ANH-0003EC-J5@mailserv.mta.ca> (raw)
Dear All,
I would need please a bibliographical reference for the following fact :
"Let C be a complete cocomplete cartesian closed category. Let I be a small
category. Then the category of functors C^I is cartesian closed."
(If Hom is the internal hom functor of C, let Hom(X_*,Y_*)=\int_i
Hom(X_i,Y_i) ; then the internal hom of C^I is defined by HOM(X_*,Y_*)_j= j
|-> Hom(X_* x 1[j], Y_*) where 1 is the terminal object of C and Z |-> Z[j]
is left adjoint to the i-th evaluation functor X_* |-> X_j)
Thanks in advance. pg.
reply other threads:[~2006-02-14 11:52 UTC|newest]
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