This is the first of several talks on the subject of classifying topoi. I began with a brief reminder of the overall picture from the first talk, i.e. what are classifying topoi and why do we care (from the point of view of organising mathematics). Then I spent some time talking about tensor products in algebra, the "non-additive" version of tensor products that arise in the context of topos theory, and how this intuition allows us to think about geometric realisation of simplicial sets, and potentially many other geometric functors between classifying topoi.
The lecture notes are available here: therisingsea.org/notes/ch2018-lecture12.pdf.
For the general seminar webpage see therisingsea.org/post/seminar-ch/.