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