This was a talk for the Junior Logic Seminar at the University of Oxford, 7th of June 2022.
Abstract. I shall investigate the modal theories and validities in a variety of cases arising from the archetypical concrete category of sets and functions. I introduce new insights into the method of control statements, answering a MathOverflow question about buttons and switches.
The MathOverflow question I am referencing is Are buttons really enough to bound validities by S4.2?