CAUTION: The Sender of this email is not from within Dalhousie. I hope this message finds you all well. The Topos Institute is very excited to announce a new seminar series: Em-Cats. This public series of virtual seminars is being launched after careful thought and planning by Eugenia Cheng, with the aim of helping the next generation of category theorists to become wonderful speakers, as well as to offer opportunities to graduate students in places where there is not a category theory group or local seminar that they can usefully speak in. The seminars will be held monthly, but do not have a regular schedule, so that speakers from different time zones can give their talk at a time that best suits them. The first talk will be on the 25th of August, at 17:00 UTC, when Jade Master is going to talk about the Universal Property of the Algebraic Path Problem (the abstract for which can be found at the end of this message). The seminar will be chaired by Martin Hyland, and will be moderated by Eugenia Cheng. We encourage all members of the community to come and listen, and to be involved in the question and social sessions after the talk. For more information, including links to the Zoom meeting and the YouTube livestream, please see the webpage: https://topos.site/em-cats <https://topos.site/em-cats> . Have a nice weekend, and we look forward to seeing you all on the 25th! Best, Tim Hosgood (Research affiliate, Topos Institute) tim@topos.institute <mailto:tim@topos.institute> ——— Jade Master: Universal Property of the Algebraic Path Problem The algebraic path problem generalizes the shortest path problem, which studies graphs weighted in the positive real numbers, and asks for the path between a given pair of vertices with the minimum total weight. This path may be computed using an expression built up from the "min" and "+" of positive real numbers. The algebraic path problem generalizes this from graphs weighted in the positive reals to graphs weighted in an arbitrary commutative semiring R. With appropriate choices of R, many well known problems in optimization, computer science, probability, and computing become instances of the algebraic path problem. In this talk we will show how solutions to the algebraic path problem are computed with a left adjoint, and this opens the door to reasoning about the algebraic path problem using the techniques of modern category theory. When R is "nice", a graph weighted in R may be regarded as an R-enriched graph, and the solution to its algebraic path problem is then given by the free R-enriched category on it. The algebraic path problem suffers from combinatorial explosion so that solutions can take a very long time to compute when the size of the graph is large. Therefore, to compute the algebraic path problem efficiently on large graphs, it helps to break it down into smaller sub-problems. The universal property of the algebraic path problem gives insight into the way that solutions to these sub-problems may be glued together to form a solution to the whole, which may be regarded as a "practical" application of abstract category theory. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]