Update: I am updating my question to be more precise.
I am studying Category of finite sets and functions (FinSet). I am aware that for some of the concepts in Set Theory there are well-known categorical counterparts:
- Cartesian Product ($A \times B$) | Product
- Disjoint Union ($ A+B $) | Co-product
- Subseting ($A \subset B$)| subObject
- PowerSet ($P(A)$) | Exponential object
I am looking to complete this list and looking to see how the following concepts are interpreted in categorical sense.
- Union ($A \cup B$) | ?
- Intersection ($A \cap B$) | ?
- Membership ($A \in B$) | ?
- Cardinality ($|A|$) | ?
- subtraction ($A - B$) | ?
- Complement ($A'$) | ?