Lecture Videos
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Session 7 Chapter 4: Co-design: Profunctors and Monoidal Categories Part 1 by Dr. David I. Spivak |
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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