IV Seminar on Categories and Applications,
Centre de Recerca
Abstract Let Wn be the space of walks on the natural numbers in which you start at position n, take one step left or right with every second that passes, and continue forever. It turns out that the sequence (Wn), taken up to isomorphism, is periodic. This is not an isolated curiosity: many similar examples of periodicity can be found, and there is a general theory of such phenomena. This involves the topology of totally disconnected spaces, the theory of rigs, and a certain class of toposes.