Lecture Videos
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Session 3 Chapter 2: Resources: Monoidal Preorders and Enrichment Part 1 by Dr. David I. Spivak |
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Session 4 Chapter 2: Resources: Monoidal Preorders and Enrichment 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 2: Resources: Monoidal Preorders and Enrichment (PDF)
2.1 Getting from \(a\) to \(b\)
2.2 Symmetric monoidal preorders
2.2.1 Definition and first examples
2.2.2 Introducing wiring diagrams
2.2.3 Applied examples
2.2.4 Abstract examples
2.2.5 Monoidal monotone maps
2.3 Enrichment
2.3.1 \(\mathcal{V}\)-categories
2.3.2 Preorders as Bool-categories
2.3.3 Lawvere metric spaces
2.3.4 \(\mathcal{V}\)-variations on preorders and metric spaces
2.4 Constructions on \(\mathcal{V}\)-categories
2.4.1 Changing the base of enrichment
2.4.2 Enriched functors
2.4.3 Product \(\mathcal{V}\)-categories
2.5 Computing presented \(\mathcal{V}\)-categories with matrix multiplication
2.5.1 Monoidal closed preorders
2.5.2 Quantales
2.5.3 Matrix multiplication in a quantale
2.6 Summary and further reading
