Real sets

Real sets

[Ross Street]

Dear Colleagues

We are sorry to say that Examples 5.5 and 5.6 in our paper

[Real sets, Tbilisi Mathematical Journal 10(3) (2017) 23--49]

are not examples of series monoidal categories afterall.
Our attempts to accommodate them are leading to interesting directions which will take awhile to finalise.
For now, in a new arXiv version of ``Real Sets'', we have pointed out that those Examples, and the dependent Examples 5.12 and 5.13, are in error. 
Nothing else in the paper depends on those examples.

George Janelidze
Ross Street

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Re: Real sets

[Peter Selinger]

Dear George and Ross,

thank you! I am aware of many papers that contain mistakes, but this
is the first time in my memory that somebody has publicly retracted an
already published result. There should be more of this. You are to be
commended.

A few years ago I published some papers in a physics journal, and I
was surprised to discover that the physicists have a completely
different system from what we have in mathematics and computer
science. A typical physics journal has several types of submissions.
The most basic one is a research paper; this is refereed in a similar
way to how we do it in math (except much faster). Another submission
type is an erratum for an existing paper. The most interesting type of
submission is a comment on somebody else's paper. If you submit such a
comment, then roughly speaking, the editor will first send your
comment to the author of the paper you are commenting on. The author
is invited to write a response to the comment. The editor will then
send your comment along with the author's response, if any, to an
anonymous referee. If the referee and the editor are satisfied, both
the comment and the response will be published. There will be a link
from the original paper to the comment and vice versa, so that people
can readily find out what has been said.

(The actual procedure is even more complicated; see e.g. here:
https://journals.aps.org/pra/authors/comments-physical-review-a)

I did a quick search and found that there seem to be about 25
comments and 25 errata for every 1000 papers published in Physical
Review A.

I am sure that this system has evolved to accommodate the scientific
method. I.e., what physicists typically publish is the result of an
experiment. Somebody else might replicate the experiment, and might
get the same result (thereby strengthening the evidence), or a
different result (thereby weakening it). In either case, this activity
is considered completely legitimate, even encouraged, as it adds to
the total body of evidence.

In math, of course, we don't usually do experiments, and our results
are supposed to be immutable. Nevertheless, I sometimes wish there
were a more efficient and tractable process by which errors in the
literature could be reported and corrected (not for the purpose of
embarrassing the authors, but to maintain and improve the quality of
the literature). Maybe in the future, some math journals will adopt a
process similar to the physics one. I think this would be a great
idea!

Best wishes for the new year, -- Peter

Ross Street wrote:
>
> Dear Colleagues
>
> We are sorry to say that Examples 5.5 and 5.6 in our paper
>
> [Real sets, Tbilisi Mathematical Journal 10(3) (2017) 23--49]
>
> are not examples of series monoidal categories afterall.
> Our attempts to accommodate them are leading to interesting directions which will take awhile to finalise.
> For now, in a new arXiv version of ``Real Sets'', we have pointed out that those Examples, and the dependent Examples 5.12 and 5.13, are in error.
> Nothing else in the paper depends on those examples.
>
> George Janelidze
> Ross Street
>



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