# 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

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).

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