labbess asked:

Can you explain to me a little about the interaction between Kate Kane and Bruce Wayne (and co.), at least recently? I have seen a lot of fanart that includes her into the so-called "Bat family" but I have yet to see any canonical evidence of this closeness.

Bruce asked her to join Batman, Inc. and she said she’d think about it and then turned him down. Kate has also worked with Dick when he was Batman.

I would really not try and relate fan art to canon.