Barry Jay recently sought comments on A^2 is cartesian closed when A is so, where 2 is the arrow-category. Roy Crole and Peter Johnstone both pointed out that this was a special case of Artin glueing. Is there not a more general fact? The forgetful 2-functor from cartesian- closed categories to categories is fairly easily seen to be monadic - the monadicity is well-known for categories with finite products or finite limits, and adding the right adjoint to (- x A) is purely equational. But for any 2-monad T on K, T-Alg has all lax and pseudo limits - indeed all flexible limits - formed as in K; see [Blackwell, Kelly, and Power, Two- -dimensional monad theory, J. Pure Appl. Algebra 50 (1989), 1-41]. Artin glueing is the case of the lax limit of a map, if I remember correctly its meaning. But (-)^X for any category X is also a flexible limit, so that Jay's observation is included directly without recourse to Artin glueing. Then, again, Michael Barr on 30 Jan asserts that A^X is cartesian closed if A is so when X is finite and A has finite limits. Surely such conditions are not needed - A^X is cartesian closed when A is so. Am I missing something? Max Kelly