Timeline for A new (?) way of composing monads
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Oct 5, 2022 at 2:23 | answer | added | Simon Henry | timeline score: 9 | |
| Oct 4, 2022 at 10:54 | comment | added | varkor | It may be irrelevant (I haven't the time to look more carefully now), but there is a more general way of composing monads than a distributive law: namely a wreath (§3 of The formal theory of monads II). It may be worth checking whether there's any relation to your situation. | |
| Oct 4, 2022 at 7:13 | comment | added | Vladimir Dotsenko | This is very intriguing. The only immediate comment is that the multiplication on $M\times L(M)$ that you obtain is something I have already seen in a linearized context: it measures to what extent the differential of the bar complex $B(A)$ of an associative algebra $A$ is not a derivation of the concatenation product imposed on the $B(A)$ (which is naturally a coalgebra, not an algebra, hence "imposed"). It leads to a non-commutative analogue of Batalin-Vilkovisky algebras, see arxiv.org/abs/1510.03261 and references therein. | |
| Oct 4, 2022 at 4:30 | comment | added | მამუკა ჯიბლაძე | Very interesting! A test case for a general construction like this would be two submonoids $M_1$, $M_2$ of a monoid $M$ such that $M_1M_2=\{m_1m_2\mid m_i\in M_i,i=1,2\}$ is a submonoid too. I believe this does not always come from (an appropriate case of) a distributive law. Does it come from your construction? | |
| Oct 4, 2022 at 3:27 | history | edited | Simon Henry | CC BY-SA 4.0 |
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| Oct 4, 2022 at 3:09 | comment | added | Benjamin Steinberg | I'll try to look it up a good reference. One issue is there are semigroup and monoid versions and usually in a way similar to the homegeneous versus nonhomegeneous bar resolution the Karnofsky-Rhodes construction will look at the sequence of edges And vertices you get in the left Cayley graph by multiplying the susccesive guys in the list and then view m' as translating the second list and doing the same. | |
| Oct 4, 2022 at 0:42 | comment | added | Simon Henry | @BenjaminSteinberg thanks for the keyword, I hadn't heard about this before and I need to look at it (I've found a few things googling, but if you have recommendations, I'd be interested) | |
| Oct 4, 2022 at 0:34 | comment | added | Benjamin Steinberg | Your monoid construction from nonempty lists (or at least a small variant of it) is used as the first step of constructing the left Karnosfky-Rhodes expansion of $M$ (with respect to the generating set $M$). Then on imposes a certain congruence. | |
| Oct 3, 2022 at 23:24 | history | asked | Simon Henry | CC BY-SA 4.0 |