Lecture Videos and Readings

Chapter 7: Logic of Behavior: Sheaves, Toposes, Languages

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Lecture Videos

Session 13

Chapter 7: Logic of Behavior: Sheaves, Toposes, Languages Part 1

by Dr. David I. Spivak

Session 14

Chapter 7: Logic of Behavior: Sheaves, Toposes, Languages 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 7: Logic of Behavior: Sheaves, Toposes, Languages (PDF)

7.1 How can we prove our machine is safe?

7.2 The category Set as an exemplar topos

7.2.1 Set-like properties enjoyed by any topos

7.2.2 The subobject classifier

7.2.3 Logic in the topos Set

7.3 Sheaves

7.3.1 Presheaves

7.3.2 Topological spaces

7.3.3 Sheaves on topological spaces

7.4 Toposes

7.4.1 The subobject classifier \(\Omega\) in a sheaf topos

7.4.2 Logic in a sheaf topos

7.4.3 Predicates

7.4.4 Quantification

7.4.5 Modalities

7.4.6 Type theories and semantics

7.5 A topos of behavior types

7.5.1 The interval domain

7.5.2 Sheaves on \(\mathbb{IR}\)

7.5.3 Safety proofs in temporal logic

7.6 Summary and further reading

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