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--- blog:2023-06-27 [2023/06/27 18:24] – [OK then, how about the weird convolution euler index] pzhou
+++ blog:2023-06-27 [2023/06/27 18:32] (current) – pzhou
@@ Line 46: / Line 46: @@
 For the abelian case, there should be several approaches, all leading to the correct consistent answers.
+BFN and VV both defined some convolution, maybe even BDG.
+==== BFN convolution space ====
+Recall what is matrix multiplication: given matrices of sizes $n_1 \times n_2$, $n_2 \times n_3$, called $M_{12}$ and $M_{23}$, we can form their product, which is given by
+$$ (M_{13})_{ij} = \sum_k (M_{12})_{ik} (M_{12})_{kj} $$
+This can be considered as composing correspondences. We need a way to do composition (multiplication), and a way to do summation (over all possible $k$, intermediate state).
+If we package this in terms of BM homology, we