Lecture Videos and Readings

Chapter 5: Signal Flow Graphs: Props, Presentations, and Proofs

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Lecture Videos

Session 9

Chapter 5: Signal Flow Graphs: Props, Presentations, and Proofs Part 1

by Dr. David I. Spivak

Session 10

Chapter 5: Signal Flow Graphs: Props, Presentations, and Proofs 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 5: Signal Flow Graphs: Props, Presentations, and Proofs (PDF)

5.1 Comparing systems as interacting signal processors

5.2 Props and presentations

5.2.1 Props: definition and first examples

5.2.2 The prop of port graphs

5.2.3 Free constructions and universal properties

5.2.4 The free prop on a signature

5.2.5 Props via presentations

5.3 Simplified signal flow graphs

5.3.1 Rigs

5.3.2 The iconography of signal flow graphs

5.3.3 The prop of matrices over a rig

5.3.4 Turning signal flow graphs into matrices

5.3.5 The idea of functorial semantics

5.4 Graphical linear algebra

5.4.1 A presentation of Mat(\(R\))

5.4.2 Aside: monoid objects in a monoidal category

5.4.3 Signal flow graphs: feedback and more

5.5 Summary and further reading

Assignment

Problem set 3 (PDF) due at the beginning of Session 14.

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