Timeline for KK-theory as a stable infinity-category and KU Mod
Current License: CC BY-SA 3.0
21 events
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| Aug 14, 2013 at 16:54 | comment | added | Rohan Lean | @Urs: I doubt that there is a satisfying absolute answer to that, but perhaps some people know many satisfying examples. I suggest that you ask that as a new question. | |
| Aug 14, 2013 at 16:54 | comment | added | Rohan Lean | @Rasmus: No, example 5.3 in the same article gives a counterexample to that. | |
| Aug 14, 2013 at 11:39 | comment | added | Rasmus | @Rohan: Perhaps the $K$-theory functor would have a chance of being strongly monoidal if one considered the maximal tensor product instead of the minimal one (both descend to $\mathrm{KK}$)? | |
| Aug 13, 2013 at 23:59 | comment | added | Urs Schreiber | Maybe I am actually just interested in the bootstrat subcategory, given that it contains the convolution algebras of amenable Lie groupoids. What's the largest class of groupoid convolution algebras in the bootstrap? | |
| Aug 13, 2013 at 23:11 | history | edited | Rohan Lean | CC BY-SA 3.0 |
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| Aug 13, 2013 at 23:09 | comment | added | Urs Schreiber | Thanks for the pointer! Concerning "natural": I just meant to exclude unwanted solutions such as the monoidal functor which is constant on the tensor unit. I don't want any monoidal functor $KK \to KU Mod$, but one that does what it is expected to do. | |
| Aug 13, 2013 at 23:02 | comment | added | Rohan Lean | @Urs: the K-theory functor cannot be strongly monoidal (c.f. arxiv.org/pdf/1111.7228.pdf, example 3.9). I am not entirely sure what you mean by ‘natural’, but I suspect that the answer is ‘no’. There is a functor between quasi-categories that covers the K-theory functor. More generic statements of this kind are part of my thesis, which is yet unfinished and unavailable. | |
| Aug 13, 2013 at 7:30 | comment | added | Urs Schreiber | @Rohan, while the pointer to Dell'Ambrogio et al that Rasmus provided is very useful, I'd still be interested in what you might have to say about the functor to $KU Mod$. Can you produce a genuine $\infty$-functor of (stable) $\infty$-categories, maybe? Also, the functor in Dell'Ambrogio et al is only lax monoidal. I am not sure if this is inevitable. Can we have a natural strongly monoidal functor $KK \to KU Mod$? | |
| Aug 13, 2013 at 7:16 | comment | added | Urs Schreiber | Hi @Rohan, thanks a bunch for the detailed reply! It is true that I heard you say something about this before a good while back, but I pretty much forget what the status of that is. Do you have a writeup? Is this in your thesis? Can you give me pointers? I'd be happy to cite this. Now I first need to read your text above. May take a bit, as I am about to hop on a plane over the ocean. But I get back to you then. | |
| Aug 13, 2013 at 4:23 | history | edited | Rohan Lean | CC BY-SA 3.0 |
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| Aug 13, 2013 at 3:53 | history | edited | Rohan Lean | CC BY-SA 3.0 |
using mathjax formatting now
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| Aug 13, 2013 at 1:10 | history | edited | Rohan Lean | CC BY-SA 3.0 |
improved formatting
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| Aug 13, 2013 at 0:58 | history | edited | Rohan Lean | CC BY-SA 3.0 |
missing math-mode terminator
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| Aug 13, 2013 at 0:53 | history | edited | Rohan Lean | CC BY-SA 3.0 |
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| Aug 12, 2013 at 23:59 | history | edited | Rohan Lean | CC BY-SA 3.0 |
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| Aug 12, 2013 at 23:31 | history | edited | Rohan Lean | CC BY-SA 3.0 |
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| Aug 12, 2013 at 23:15 | comment | added | Ricardo Andrade | Dear @Rohan: Your answer appears to contain hard-coded bold symbols, subscripts, etc. It does not even render in an alternative but well developed browser which I use. Mathjax is not meant for highlighting math, it is meant to make sure that math will display correctly and not break randomly. I believe your current code for this answer is likely to cause several problems. I have created a meta thread at meta.mathoverflow.net/questions/624/… | |
| Aug 12, 2013 at 23:08 | history | edited | Rohan Lean | CC BY-SA 3.0 |
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| Aug 12, 2013 at 23:03 | history | edited | Rohan Lean | CC BY-SA 3.0 |
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| Aug 12, 2013 at 22:40 | review | First posts | |||
| Aug 12, 2013 at 22:50 | |||||
| Aug 12, 2013 at 22:24 | history | answered | Rohan Lean | CC BY-SA 3.0 |