Paul Levy - What Is a Monoid?

See the paper at https://dl.acm.org/doi/10.1145/3776727

First a presentation at POPL 2026.

My comment:

23:35 You have to get this far to see what they're actually doing! At 28:45 you start to wonder though,... 😂 I think one of these is a synthetic view and the other is analytic, though in Category theory it often isn't obvious which is which!

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Then a more recent one at Topos Institute: 

Subscribe to Topos Institute. 

Here's what seems like a good introduction to call-by-push-value:

Here's a longer one:

This thing turns up in a kind of congruence relation of effects:

See Levy's 2006 Jumbo λ-calculus (ref https://dl.acm.org/doi/10.1007/11787006_38). 

1:04:27 There is a categorical semantics of CBPV using adjunctions. 

Adding fixpoints and "a mild extension of CBPV using a comonadic modality"

See Emily Riehl and Terrence Tau on The Future of Mathematics. 

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