Koszul duality and Morita categories

By AHMAD · Published 28 Aug 2026 · Updated 1 Sep 2026

Link: https://arxiv.org/html/2608.27450v1

This was an interesting paper, albeit BEING slightly daft, I had very little idea on what I was reading.

"This was proving (∞,2)Categorical version of Koszul duality for operads and cooperads in spectra"

Now this is quite simple. If you have a recipe book and there's instructions to combine multiple ingredients. These are called an operad, and a cooperad is basically the opposite of an operad.

Koszul duality is the discovery that these two rulebooks are mirror images of each other.

By showing that there is an equivalence between a Morita category of operads and bimodules and a dual Morita category of cooperads and bicomodules. This result subsumes various forms of operadic Koszul duality present in the literature.

and it goes on...