* Bibliographical reference needed
@ 2006-02-14 11:52 Philippe Gaucher
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From: Philippe Gaucher @ 2006-02-14 11:52 UTC (permalink / raw)
To: categories
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.
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