Timeline for Monoid objects constructed from duals
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 4, 2021 at 13:56 | comment | added | Chris Heunen | See Lemma 4.11 and further in global.oup.com/academic/product/… | |
| Jan 3, 2021 at 20:50 | comment | added | Maxime Ramzi | $X\otimes X^*$ is also known as the internal hom of $X$; and you can prove more generally that $\hom(Y,Z)\otimes \hom(X,Y)\to \hom(X,Z)$ is "associative" in a monoidal closed category - this has appeared somewhere on MO or MSE - more specifically here : mathoverflow.net/questions/21382/… (you then need to compare your map on $X^*\otimes X$ to the one on $\hom(X,X)$) | |
| Jan 3, 2021 at 20:45 | comment | added | Qiaochu Yuan | Yes, it's correct. Associativity is easiest to prove using string diagrams; a bicategorical version of this argument shows that an adjunction gives rise to a monad (and in particular you don't need an assumption about left vs. right duals). The monoid structure you get this way is an enriched endomorphism object of $X$ with respect to a (partial) enrichment of $M$ over itself, generalizing the familiar case of $\text{FinVect}$. | |
| Jan 3, 2021 at 20:09 | history | edited | Jake Wetlock | CC BY-SA 4.0 |
added 57 characters in body
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| Jan 3, 2021 at 19:55 | history | asked | Jake Wetlock | CC BY-SA 4.0 |