Chapter 1: Generative Effects: Orders and Adjunctions Part 1
by Dr. David I. Spivak
Chapter 1: Generative Effects: Orders and Adjunctions Part 2
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).
Chapter 1: Generative Effects: Orders and Adjunctions (PDF)
1.1 More than the sum of their parts
1.1.1 A first look at generative effects
1.1.2 Ordering systems
1.2 What is order?
1.2.1 Review of sets, relations, and functions
1.2.3 Monotone maps
1.3 Meets and joins
1.3.1 Definition and basic examples
1.3.2 Back to observations and generative effects
1.4 Galois connections
1.4.1 Definition and examples of Galois connections
1.4.2 Back to partitions
1.4.3 Basic theory of Galois connections
1.4.4 Closure operators
1.4.5 Level shifting
1.5 Summary and further reading
Problem set 1 (PDF) due at the beginning of Session 6.