Timeline for Fixed objects of the M endofunctor on category Meas
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Dec 27, 2012 at 7:17 | comment | added | Tom LaGatta | For others who are as unfamiliar with monads as I am, here is a nice video by the Catsters, featuring Eugenia Cheng presenting the basics of monads: youtube.com/… h/t @Joey Hirsh | |
| Dec 27, 2012 at 4:16 | answer | added | Tom LaGatta | timeline score: 2 | |
| Dec 26, 2012 at 21:30 | answer | added | Will Sawin | timeline score: 4 | |
| Dec 26, 2012 at 21:02 | comment | added | Tom LaGatta | @Will: I am perfectly happy to accept infinite measures; I have updated my question to say extended-real-valued measures. Unfortunately, I am not familiar enough with category theory (and monads in particular) to understand your response. Could you write out a longer answer describing the monad structure present? | |
| Dec 26, 2012 at 20:58 | history | edited | Tom LaGatta | CC BY-SA 3.0 |
added 9 characters in body
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| Dec 26, 2012 at 20:33 | comment | added | Will Sawin | This functor is a monad, assuming the measures involved are allowed to take the value $\infty$. The identity sends a point to the atomic measure with mass $1$ at that point. The multiplication sends a measure on the space of measures to its integral. The two coherence conditions arise because we can reverse the order of integration of nonnegative functions without issue, and because the integral of a function against the atomic matter with mass $1$ is just the evaluation of that function. I do not know if their is a natural monad structure without infinities involved. I presume not. | |
| Dec 26, 2012 at 20:24 | comment | added | Will Sawin | I think $\mathbb R$ should be a fixed object, since a measure on $\mathbb R$ is a countable sequence of real numbers satisfying certain inequalities, which we can easily encode as a single real number. | |
| Dec 26, 2012 at 20:23 | history | edited | Tom LaGatta | CC BY-SA 3.0 |
edited title
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| Dec 26, 2012 at 19:59 | history | asked | Tom LaGatta | CC BY-SA 3.0 |