In the Batman comics and various adaptations, Batman's relationship with Poison Ivy is complex, but it can be described as more of a conflict than an obsession. Poison Ivy is a well-known supervillainess in the Batman universe, and her main goal is often centered around her love and obsession with plants and nature.
While Batman does encounter Poison Ivy regularly as one of his adversaries, his primary focus is to stop her criminal activities and protect Gotham City. Batman is portrayed as a detective and crime-fighter who dedicates his life to fighting against all sorts of threats, including supervillains like Poison Ivy.
There have been story arcs where Poison Ivy's powers and charisma have affected Batman in different ways, leading to moments of confusion or vulnerability. However, these instances are more about the challenges she poses as a villain rather than Batman being genuinely obsessed with her.
Overall, Batman's relationship with Poison Ivy can vary depending on the specific storyline or interpretation, but it is typically characterized by conflict, as he strives to uphold justice and protect his city from her villainous actions.