I'm a newbie in both formal mathematics and theoretical computer science, so please bear with me if you find my question is not properly framed. Object Oriented Modeling seems very useful in defining complex interactions when simulating real world. But it's mostly used in programming. I was wondering if we have a similar concept in mathematics. When we're doing programming, we can understand the concept of "Objects" and "Object Oriented Programming" and just implement it. But do we have formal definition of "Objects" in terms of Set Theory? Or for that matter, any other formal mathematical theory?
Can we implement/ formally define three primary object orient modeling concepts- 1. Encapsulation 2. Inheritance 3. Polymorphism
I know question is too broad, but would really appreciate if you can provide some pointers as well so that I can understand these concepts better.