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Post AjOI4uPXRV7fp2UC5A by [email protected] |
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More posts by [email protected] |
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Post #AjMAqtcIVj4FJFuBcG by [email protected] |
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Hard-core math tweet: heaps.You may have seen analogy puzzles like"swim is… |
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Post #AjMBtY0JQFlD6NxxUu by [email protected] |
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@johncarlosbaez do you not also need the axiom t(t(a,b,c),d,e)=t(a,t(d,c,b),e)? |
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Post #AjMCEyfLUPepsDNTpQ by [email protected] |
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@joshuagrochow - if that axiom is true for heaps coming from groups, it must so… |
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Post #AjMCw8krr26hcGXfxQ by [email protected] |
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@johncarlosbaez I ran across a group-like structure recently, where a relation … |
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Post #AjMCw8qtUcvZuxMULo by [email protected] |
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@leon_p_smith - hmm, so this is more like a riddle than a math problem of the u… |
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Post #AjMD1p1i7IjSAR8652 by [email protected] |
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@johncarlosbaez The last paragraph got me curious. At first, I believed that th… |
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Post #AjMD3eUKGllS3uO2s4 by [email protected] |
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@johncarlosbaez hey, no fair reading my original post before I edited it :P.(I … |
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Post #AjME0zwu7bcbhv3Jgm by [email protected] |
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@johncarlosbaez Ah, I was thinking of a semiheap (where you don't have the … |
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Post #AjMG1U7O9ZuPBRJfYe by [email protected] |
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@leemph - we should be getting the global category of torsors here unless somet… |
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Post #AjMGE6MfmOmlHITuwy by [email protected] |
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@joshuagrochow - I did not write the "simplicity" line; in fact I wat… |
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Post #AjMJ8gUwp5s7T8ScF6 by [email protected] |
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@johncarlosbaez interesting, I didn’t know this concept - the group is someho… |
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Post #AjMKDZG7GX5CQ2PpNA by [email protected] |
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@johncarlosbaez oh I see... maybe, shuffling the notation a little bit, for the… |
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Post #AjMKUpSAJCUpZGHYhs by [email protected] |
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@boarders - yes, that's a great example! Thanks! Drawing the fourth vect… |
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Post #AjMKcdf02SLZJE0duK by [email protected] |
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@leemph - so do you think we're doing the Grothendieck construction to get … |
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Post #AjMKs4Mf2FJITTn0gi by [email protected] |
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@johncarlosbaez I’m not sure, it is interesting to think about - an example y… |
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Post #AjMNWsw4dEzgoGwZV2 by [email protected] |
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@johncarlosbaez that's basically my question. The question is: how the nlab… |
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Post #AjMOIR6HQUoANcOLh2 by [email protected] |
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@leemph - well, if I had to guess a definition of the morphisms in Tors I'd… |
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Post #AjMQQ4fCves11EUyfI by [email protected] |
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@johncarlosbaez It seems so to me, at first sight. A map of sets with your prop… |
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Post #AjMl7yrbquuEr6VsWW by [email protected] |
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@johncarlosbaez I guess the forgetful functor from groups to heaps has a left a… |
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Post #AjMspXHCTvvpiSCO24 by [email protected] |
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@johncarlosbaez @joshuagrochow if this is really just the same as a torsor, wou… |
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Post #AjNeN52Mg1jDpCkygq by [email protected] |
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@francisbrb @joshuagrochow - a heap is not the same as a torsor, it's the s… |
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Post #AjNer6GCh3ZWJ2Xo8G by [email protected] |
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@OscarCunningham - the nLab describes a functor from groups to heaps called &qu… |
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Post #AjNg6Nn9tTf2ydoH9k by [email protected] |
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@johncarlosbaez I don't think Str is the left adjoint I'm thinking of. … |
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Post #AjNhNIWKqUXTVOZQki by [email protected] |
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@johncarlosbaez OK, I believe it isn't the grothendieck construction becaus… |
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Post #AjNpCspQJSGYYn2mGW by [email protected] |
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@johncarlosbaez Aha! For heaps I am pretty sure the left adjoint is the free pr… |
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Post #AjNpCsvnvjN0sa1sDA by [email protected] |
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@OscarCunningham - thanks! I'm familiar with how the free vector space on … |
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Post #AjO0Qm31Q29D52ELzM by [email protected] |
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@leemph - thanks, you're right. Which group homomorphisms ϕ: G → G'… |
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Post #AjO3xZR9csXLO4qfOi by [email protected] |
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@johncarlosbaez @boarders interestingly, in word2vec there are two different wa… |
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Post #AjO69TuEDSNJcHFrXM by [email protected] |
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@johncarlosbaez oh! I believe I know this. When I'm off work, on the subway… |
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Post #AjO9Hrb8JUBjH70n0i by [email protected] |
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@Pashhur @boarders - very interesting that they're using a spherical geomet… |
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Post #AjO9KUTejQ3iR7lcUC by [email protected] |
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@leemph - I was afraid of that: only an iso. But it is what it is! |
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Post #AjOAiC4CvtBkF2jKaW by [email protected] |
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@johncarlosbaez @boarders I never actually saw a study that measures quality of… |
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Post #AjOCi0ukb6A9YqLgBM by [email protected] |
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@Pashhur - right, I noticed that because of the relationship between groups and… |
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Post #AjOG9FF3jfV5g7WZEW by [email protected] |
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@johncarlosbaez @francisbrb but, even if people often have in mind a fixed G wh… |
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Post #AjOI4uPXRV7fp2UC5A by [email protected] |
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@johncarlosbaez forgive me, was at work and tried to do the proof in my head...… |
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Post #AjOLQZIGw6PUYt6gkq by [email protected] |
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@johncarlosbaez I hope I understand the question. When φ:G—>G' "… |
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Post #AjOPC6pCNyuu1srvlY by [email protected] |
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@leemph - I'll have to get back to you on this, I'm a bit slow when it … |
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Post #AjOXCAfisi0vauye00 by [email protected] |
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@johncarlosbaez oh, I'm sorry, you don't need to. I didn't mean to … |
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Post #AjOlTRhyC1hqiF9xE8 by [email protected] |
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@Pashhur @johncarlosbaez @boarders > I don't think there's a preferr… |
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Post #AjOlTRoLoIoJ2293Am by [email protected] |
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@buster - I agree with everything you say except perhaps the absence of a "… |
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Post #AjPzXGCqUZU2iMH4s4 by [email protected] |
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@johncarlosbaez Claim: the ways we can lift a given group homomorphism φ:G—&… |
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Post #AjQybDwwuxE64w7omm by [email protected] |
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@johncarlosbaez @Pashhur @boarders (I think my 𝑛 and yours are off-by-one! W… |
