I would like to add some logic to the insert and update events of some EF objects. I have a MVC application with category object which has a property which is a slugified ve
No there is no such extension point because your entity is POCO - it is not aware of its persistence. Such logic must be triggered in data access layer which is aware of persistence. DbContext API offers only overriding of SaveChanges.
You can expose custom events or methods on your entities and call them during processing in SaveChanges.