Lecture Videos and Readings

Chapter 6: Circuits: Hypergraph Categories and Operads

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Lecture Videos

Session 11

Chapter 6: Circuits: Hypergraph Categories and Operads Part 1

by Dr. David I. Spivak

Session 12

Chapter 6: Circuits: Hypergraph Categories and Operads Part 2

by Dr. Brendan Fong

Readings

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 6: Circuits: Hypergraph Categories and Operads (PDF)

6.1 The ubiquity of network languages

6.2 Colimits and connection

6.2.1 Initial objects

6.2.2 Coproducts

6.2.3 Pushouts

6.2.4 Finite colimits

6.2.5 Cospans

6.3 Hypergraph categories

6.3.1 Frobenius monoids

6.3.2 Wiring diagrams for hypergraph categories

6.3.3 Definition of hypergraph category

6.4 Decorated cospans

6.4.1 Symmetric monoidal functors

6.4.2 Decorated cospans

6.4.3 Electric circuits

6.5 Operads and their algebras

6.5.1 Operads design wiring diagrams

6.5.2 Operads from symmetric monoidal categories

6.5.3 The operad for hypergraph props

6.6 Summary and further reading

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