Lecture Videos
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Session 13 Chapter 7: Logic of Behavior: Sheaves, Toposes, Languages Part 1 by Dr. David I. Spivak |
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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