Polarities (Part 5)

Today I’d like to dig a little deeper into some ideas from Part 2. I’ve been talking about causal loop diagrams. Very roughly speaking, a causal loop diagram is a graph with labeled edges. I showed how to ‘pull back’ and ‘push forward’ these labels along maps of graphs. But it turns out that to make pulling back and pushing forward functorial, we need to take two very different approaches to graphs with labeled edges:

We can ignore the meaning of the edge labels—treat them as elements of an...