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Notes chapter 3
Piotr Paradziński edited this page Apr 28, 2020
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| category theory | database theory |
|---|---|
| category | database schema |
| functor C -> Set | database (instance) |
| functor C1 -> C2 | mapping between database schema C1 and C2 |
| adjoint functors | data migration |
- morphisms are columns:
- FK (morphisms between tables)
- regular column is morphisms from table to String, Int, ...
- PK identity morphisms
- objects: tables
- hom set: ???
Def A category C consists of:
- class (can be sth larger than set) of objects Ob(C)
- for every two objects a,b set of morphisms from c to d
- identities TODO
- composition rule TODO such that TODO
Remarks:
- Change of FK everywhere in DB (don't change data), change of non FK column (modification of data); DBMS theory reverse: never change FK, change other columns as you wish (sic !)
- objects = (elements, structure, properties), morphisms (sends elements -> elements and preserve structure); properties dissapear
in posets - properties: (reflexivity, transitivity); structure - order
in Cat - identities and associativity dissapears