Ummmmmmm *chuckles* Nope. No, he is not.
the batman hates' the joker and cat woman.
Batman Returns
They dated a little bit in Batman returns.
Because she was inspired by Batman to take on a theme as a cat burglar.
Cat women is a comic book charcter also in the batman movie
There is no hard data on who would win a fight between Batman and Cat woman, but she is quick and a cat and fights dirty. but men are stronger so it could be a fair fight.
none
How To Batman - 2009 How to Cat Daddy 3-20 was released on: USA: 22 November 2010
Cat woman
CollegeHumor Originals - 2006 Batman vs Cat Lady - 1.406 was released on: USA: 11 December 2012
The Batman - 2004 The Cat the Bat and the Very Ugly 2-1 was released on: USA: 14 May 2005
The New Batman Adventures - 1997 Cult of the Cat 2-3 was released on: USA: 18 September 1998