Timeline for Is the bicategory of sets and relations a Markov category?
Current License: CC BY-SA 4.0
11 events
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| Nov 23, 2021 at 15:42 | comment | added | xuq01 | I have no answer to this question because I don't know what a Markov 2-category would be, but I'm interested in working on this problem. | |
| Nov 22, 2021 at 16:53 | history | edited | mathlete42 | CC BY-SA 4.0 |
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| Nov 22, 2021 at 5:41 | comment | added | David Roberts♦ | OK, thanks for the clarification. Thankfully, $\mathbf{Rel}$ is a (1,2)-category (it is poset-enriched, not category-enriched, so questions of coherence for a 2-categorical version of a Markov category will not be so scary. | |
| Nov 22, 2021 at 5:05 | history | edited | mathlete42 | CC BY-SA 4.0 |
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| Nov 22, 2021 at 5:02 | comment | added | mathlete42 | @DavidRoberts Thanks for the questions. I am interested to know if the 2-category, along with it's 2-morphisms is Markov, and so I guess I am wondering about the bicatecory version of Markov category. | |
| Nov 22, 2021 at 0:58 | comment | added | David Roberts♦ | Do you mean a bicategorical version of Markov category? Or a truncation of Rel to a 1-category? And if the first, do you mean the definition of $\mathbf{Rel}$ as a 2-category at ncatlab.org/nlab/show/Rel#definition ? | |
| Nov 22, 2021 at 0:58 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
formatting, paper title, typo
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| Nov 22, 2021 at 0:54 | comment | added | David Roberts♦ | @YCor that is the standard interpretation of what the question is asking, it's not a type mismatch, past phrasing the answer as "yes, using the [blah] monoidal structure" (if this is the case). | |
| Nov 22, 2021 at 0:13 | comment | added | YCor | If I read the Fritz link, I read that a Markov category is a category endowed with some additional structure (symmetric monoidal + ...). So given a category, the question "is this a Markov category" doesn't make sense (as "is this topological space a category?" is senseless). The closest I could imagine is whether it admits such a structure (which might be or not be unique). Is it the desired meaning of the question. | |
| Nov 22, 2021 at 0:09 | history | edited | YCor | CC BY-SA 4.0 |
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| Nov 21, 2021 at 21:16 | history | asked | mathlete42 | CC BY-SA 4.0 |