Re: About the cartesian closedness of the category of all small diagrams

For a fibration of ccc's over a ccc one knows that the total category is again ccc and this structure is preserved (could be in Bart Jacob's book). As to (1) even if K = Set we know that the Set^C are ccc's (actually toposes) but reindexing in general doesn't preserve the ccc's structure since in Set^C the exponentials are not computed pointwise (unless C is discrete). It already goes wrong when C is the ordinal 2. Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]