by Dr. David I. Spivak
by Dr. Brendan Fong
Internal links in the chapter file below are non-functional. For working links, open the file for the full textbook: An Invitation to Applied Category Theory: Seven Sketches in Compositionality (PDF - 2.6MB).
3.1 What is a database?
3.2.1 Free categories
3.2.2 Presenting categories via path equations
3.2.3 Preorders and free categories: two ends of a spectrum
3.2.4 Important categories in mathematics
3.2.5 Isomorphisms in a category
3.3 Functors, natural transformations, and databases
3.3.1 Sets and functions as databases
3.3.3 Database instances as Set-valued functors
3.3.4 Natural transformations
3.3.5 The category of instances on a schema
3.4 Adjunctions and data migration
3.4.1 Pulling back data along a functor
3.4.3 Left and right pushforward functors, \(\Sigma\) and \(\Pi\)
3.4.4 Single set summaries of databases
3.5 Bonus: An introduction to limits and colimits
3.5.1 Terminal objects and products
3.5.3 Finite limits in Set
3.5.4 A brief note on colimits
3.6 Summary and further reading
Problem set 2 (PDF) due at the beginning of Session 10.