\minihead{Cartesian closed categories} We have seen that for every set $ B $ , there is an adjunction $ ( - \times B) \dashv ( - )^B $ (Example X), and that for every category $ \mathscr{B} $ , there is an adjunction $ ( - \times \mathscr{B}) \dashv \ftrcat{\mathscr{B}}{ - } $ (Remark X).A category $ \mathscr{A} $ is cartesian closed if it has finite products and for each $ B \in \mathscr{A} $ , the functor $ - \times B{\colon}\linebreak[0] \mathscr{A} \to \mathscr{A} $ has a right adjoint. We write the right adjoint as $ ( - )^B $ , and, for $ C \in \mathscr{A} $ , call $ C^B $ an exponential. We may think of $ C^B $ as the space of maps from $ B $ to $ C $ .