Lecture Videos and Readings

Chapter 4: Co-design: Profunctors and Monoidal Categories

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Lecture Videos

Session 7

Chapter 4: Co-design: Profunctors and Monoidal Categories Part 1

by Dr. David I. Spivak

Session 8

Chapter 4: Co-design: Profunctors and Monoidal Categories 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 4: Co-design: Profunctors and Monoidal Categories (PDF)

4.1 Can we build it?

4.2 Enriched profunctors

4.2.1 Feasibility relationships as Bool-profunctors

4.2.2 \(\mathcal{V}\)-profunctors

4.2.3 Back to co-design diagrams

4.3 Categories of profunctors

4.3.1 Composing profunctors

4.3.2 The categories \(\mathcal{V}\)-Prof and Feas

4.3.3 Fun profunctor facts: companions, conjoints, collages

4.4 Categorification

4.4.1 The basic idea of categorification

4.4.2 A reflection on wiring diagrams

4.4.3 Monoidal categories

4.4.4 Categories enriched in a symmetric monoidal category

4.5 Profunctors form a compact closed category

4.5.1 Compact closed categories

4.5.2 Feas as a compact closed category

4.6 Summary and further reading

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