I’ll guess what is meant is that you take the inverse images of measurable sets of $[0, 1]$, which gives you a $\sigma$-algebra on $G(X)$.

]]>In the formula for the multiplication of the Giry monad (why is it called the “counit”?), what is P(X) in the integral? P(X) is only defined well below this formula. It looks like the formula should actually say G(X), not P(X).

The relevant change is Revision 23 by K. Sturtz on October 30, 2018.

]]>Between #21 and #28, there was discussion of additions by Sturz. He’s now brought out a new paper on Giry algebras over measurable spaces. Any views?

- Kirk Sturz,
*The existence and utility of Giry algebras in probability theory*, (arXiv:2006.08290)

With all this attention being paid to categorical probability theory now, surely some expert out there could help.

]]>I corrected the monadic part of the history.

]]>I have taken the liberty of turning the footnote into an item in the list if references – because that’s what it is and how you are using it in the text. Then I replaced the unspecified “in a video comment” with actual pointer to that reference.

(Am relieved to hear that the Pentagon doesn’t disagree with the category of probabilistic mappings.)

]]>Added a transcript of Lawvere’s comments.

]]>I removed the reference to personal communication with me since we also have the video. Added that Lawvere’s appendix was intended as a framework for verification protocols on arms control

]]>Dmitri Pavlov wrote at #35:

I feel like some part is missing from this story. Why was it attached as an appendix to this unrelated report?

Apparently this appendix was intended to provide a reasonable framework for the development of verification protocols in the arms control context. We also have Lawvere on video telling the story himself! I will add this link to the page.

]]>have moved the “History”-section from being the second to being the second-to-last one (i.e. right before the references).

Changed the very first line of the entry from

The

Giry monad(Giry 80) …

to

]]>The

Giry monad(Giry 80, following Lawvere 62)

40: according to vague memory it was this Dortmund preprint Characterizing the Eilenberg-Moore algebras for a monad of stochastic relations, listed at Giry monad. In any case it was not from a journal but a preprint of similar look and the content fits.

]]>I remember discussing one Doberkat’s paper on stochastic stuff and Giry monads and generalizations with Roland Fridrich at the time, actually several years earlier. Later Doberkat had some new articles which touched the topic and I got hold of the book only later. Which was original viewed, I should look at time stamps in my old directories. I can not do in the very moment, but I will check this later, thanks.

]]>About Michèle Giry, I met her just once in Madame Ehresmann’s office in Amiens. I believe she became a secondary school teacher and then went into teacher training. She used to have a webpage in the University of Amiens but that link is now dead so I presume she has retired.

]]>This reference seems to have been added by Zoran in May 2013, which is over a year from the last Wayback machine capture, so it’s conceivable the items were renumbered, though *Coalgebraic Logic Over General Measurable Spaces – A Survey* is the best bet for what was meant. I may have a look tomorrow at the article to see if it is even relevant, if Zoran (or someone else) doesn’t pipe and correct me.

OK, so “item 5” in this Internet Archive capture is

- E.-E. Doberkat, Ch. Schubert: Coalgebraic Logic Over General Measurable Spaces – A Survey. Math. Struct. Comp. Sci. 21 (2), 2011, 175 - 234 (pdf). We discuss in this survey the generalization of stochastic Kripke models for general modal logics through predicate liftings for functors over general measurable spaces. Results on expressivity are derived, and it is shown that selection arguments permit incorporating the discussion of bisimilarity, provided the underlying spaces are assumed to be Polish.

which doesn’t look right. Looking at those entries that mention ’Eilenberg’ or ’Giry’, it’s hard to tell which, if any, our article is meant to be describing.

]]>Updating various references with journal links etc.

]]>It’s been there right from the start rev 1.

]]>Can we do something about this abomination of a non-reference?

Doberkat has a longer article on Eilenberg-Moore algebras of the Giry monad as item 5 here. (Unfortunately, the monograph ‘Stochastic Relations: Foundations for Markov Transition Systems’ doesn’t appear to be available.)

now that link is broken, it is useless. Why not give the name? Was item 5 the named paper or something else? What if the numbering had changed?

*Edit:* the monograph *is* available, as a book for purchase: https://books.google.com.au/books/about/Stochastic_Relations.html?id=_OmI_xrYqawC&redir_esc=y, so this sentence makes one think it is nowhere available. I will edit the page to fix this, but not now. I will see if I can track anything down about the mysterious “item 5”, if no one else knows what it might be.

Sorry, confused correspondence with Sturtz by correspondence with Tobias Fritz. Corrected now.

]]>Actually, the footnote created only a mess, because Tobias had already elaborated in the reference section. Added a link instead.

]]>I have added to the text pointer to the reference in question.

Can we give poor Michèle Giry a hyperlink?

I suggest to move the section “History” from the top to the bottom of the entry. This is distractive miscellenania barely on topic, which the reader should not need to skip through to find out what a Giry monad is in the first place.

]]>Footnote added.

Anonymous

]]>I feel like some part is missing from this story. *Why* was it attached as an appendix to this unrelated report?

I think that would be good.

]]>