18.S097 | January IAP 2019 | Undergraduate

Applied Category Theory

Lecture Videos and Readings

Chapter 2: Resources: Monoidal Preorders and Enrichment

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Lecture Videos

Session 3

Chapter 2: Resources: Monoidal Preorders and Enrichment Part 1

by Dr. David I. Spivak

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 V-categories

2.3.2 Preorders as Bool-categories

2.3.3 Lawvere metric spaces

2.3.4 V-variations on preorders and metric spaces

2.4 Constructions on V-categories

2.4.1 Changing the base of enrichment

2.4.2 Enriched functors

2.4.3 Product V-categories

2.5 Computing presented 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

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January IAP 2019
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