Maths - Sheaf Example - Database

This is an example for the page about sheaves which is here.

Example - Relational Database

This could be a generalisation of the sheaf concept.

Here Cop is a database schema.

This imposes a structure on the sets which are the database tables.

See simplical databases.

diagram of database

Relational databases link tables by having shared keys.

This gives a structure to the table which must play well with the structure of the schema.

diagram database keys

As an example here are some key values.

In this case a mapping from T1 to T2 is injective which corresponds to T2 being a subset of T1.

Relational databases have many to one relationships between tables. For instance part of census data may have

  • A table with an entry for each person.
  • A table with an entry for each residence.

There might then be a many to one relationship between these two tables.

More information about relational databases on page here.

diagram fibre as database
In order to implement many to many relationships between tables we need to insert an extra table between them: diagram



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see also:

Michael Robinson - Youtube from two-day short course on Applied Sheaf Theory:

  1. Lecture 1
  2. Lecture 2 - about simplicies & topology (sound on video is not good - quiet and delayed)
  3. Lecture 3
  4. Lecture 4
  5. Lecture 5
  6. Lecture 6
  7. Lecture 7
  8. Lecture 8
Correspondence about this page

Book Shop - Further reading .

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

cover Introduction to Topological Manifolds (Graduate Texts in Mathematics S.)

Other Books about Curves and Surfaces

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