What's the relation between OOP and category theory?
There are absolutely some relationships between the semantics and practice of OOP and category theory. This is somewhat unsurprising since both fields attempt to give a principled generic account of structure and behavior in a synthetic manner.

The most apparent work I am aware of is the categorical semantics of UML, which is admittedly different from OOP in the large, but I think captures much of the crux of the debate on the semantics of objects themselves. One example is Zinovy Diskin's Mathematics of UML.