14 Feb
2006
14 Feb
'06
11:52 a.m.
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.