Timeline for Recognition theorem for a functor (bi)category or category of monads?
Current License: CC BY-SA 4.0
11 events
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| Nov 26 at 23:21 | comment | added | Ilk | Yea, i think Mnd(K) in isolation is what am looking for, so that seems to be an open problem, if am reading Lack-Miranda and citation right, which would answer my question as we dont know | |
| Nov 26 at 19:47 | comment | added | varkor | Lack–Miranda's paper characterises the inclusion $\text{Mnd}(X) \to \text{EM}(X)$, so it is not helpful if you want to characterise $\text{Mnd}(X)$ in isolation. | |
| Nov 26 at 19:26 | comment | added | Ilk | @varkor Oh I was recently skimning the Lack-Miranda What is the universal property of the 2-category of monads?, but I didn't grok it. That might actually be the answer to my question. | |
| Nov 26 at 18:56 | comment | added | varkor | Yes, I mean the completion under Eilenberg–Moore objects, which can be characterised by virtue of being a free completion under a class of weighted limits, e.g. in §4 of Kelly–Schmitt's Notes on enriched categories with colimits of some class. | |
| Nov 26 at 18:33 | comment | added | Ilk | @varkor not directly relevant i think, but i am curious to know about this characterization. The motivation here is getting a handle on possibility of reduction for an extension of your RMnd(j) with a notion of 2-cell to Mnd(K) for some bicategory K in the non-dense case. Is the characterization of EM(X) you have in mind, the one as Eilenberg-Moore completion, or some other one? Timo | |
| Nov 26 at 18:18 | comment | added | varkor | I'm not sure whether it's relevant to you, but it is possible to characterise the bicategory $\text{EM}(X)$, whose objects and 1-cells are the same as those of $\text{Mnd}(X)$, but whose 2-cells are more general. Depending on your motivation, this might be just as good. | |
| Nov 26 at 17:30 | history | edited | Ilk | CC BY-SA 4.0 |
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| Nov 26 at 17:21 | history | edited | Ilk | CC BY-SA 4.0 |
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| Nov 26 at 16:36 | history | edited | YCor | CC BY-SA 4.0 |
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| Nov 26 at 16:07 | history | edited | Ilk | CC BY-SA 4.0 |
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| Nov 26 at 16:01 | history | asked | Ilk | CC BY-SA 4.0 |