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Sep 27, 2021 at 9:31 vote accept Lilolance
Sep 24, 2021 at 16:51 comment added Vladimir Dotsenko @Lilolance I strongly suggest to write explicitly what the parallel axiom means for a cooperad; this hopefully will explain in a definitive way why terms appear in pairs.
Sep 24, 2021 at 14:40 comment added Lilolance Thank you for answering! I did indeed draw these using trees, but I do not see where the second half of the pair comes from in the calculation $(d^r_\alpha)^2$? We have that $(c_{(11)} \circ_i c_{(12)} ) \circ_j c_{(2)}$ appears exactly once for every $i$ and $j$
Sep 24, 2021 at 12:49 history answered Vladimir Dotsenko CC BY-SA 4.0