In this talk, I will explore the connection between algebraic language theory and topos theory, focusing on why algebraic language theory is appealing to topos theorists—or at least to me. I will begin by introducing toposes as a simultaneous generalization of topological spaces and monoids. Then, I will construct the topos of automata, the topos of regular languages, and the toposes of other language classes. Finally, I will discuss what topos theory might offer to automaton theory, particularly in relation to “geometric invariants” in topos theory.
Date and Venue
Start Date
Venue
Zoom link
End Date
Speaker
Ryuya Hora
Speaker's Institution
University of Tokyo
Files
semLP_2.pdf113.23 KB
Area
Semigroups, Automata and Languages