Timeline for What is the (Co)Monad for a Bag
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Jan 27, 2018 at 8:29 | comment | added | Peter Heinig | ''occurrence set'', ''heap'', ''sample'', and ''fireset'' --finitely repeated element set.'' Apart from the formalization via free commutative monoids, the most usual formalization within usual set theory is 'multiset'='function from a set to $\omega$', with each function value interpreted as the multiplicity. | |
| Jan 27, 2018 at 8:25 | comment | added | Peter Heinig | Since, unbelievably, no one has done so yet, let me point out the obvious and record the usual: Tom Leinster's above comment is entirely correct. Some usual terminology has not been mentioned yet: the most usual synonym for 'bag' in mathematics theses days is multiset. To give a reference, let me cite [W. D. Blizard: Multiset Theory. Notre Dame Journal of Formal Logic, Vol. 30, No. 1, 1989; p. 37]: ''The word ''multiset'' [...] which abbreviates the term ``multiple-membership set'', is now the commonly accepted name for this concept, replacing ''bag'', ''bunch'', ''weighted set'', [...] | |
| Jan 27, 2018 at 8:06 | comment | added | მამუკა ჯიბლაძე | I've tried to make one of them look as monoid monad as much as possible in Lower bagdomain as a glueing | |
| Jan 27, 2018 at 8:04 | comment | added | მამუკა ჯიბლაძე | There are lower and upper bagdomain monads on toposes studied by Vickers and Johnstone - see e. g. Partial products, bagdomains and hyperlocal toposes by the latter. As the name suggests, value of this monad is bags of one sort or other. Several other possibilities are in Variations on the bagdomain theme. | |
| Jan 26, 2018 at 23:49 | vote | accept | Ben Sprott | ||
| Jan 26, 2018 at 22:56 | answer | added | Wouter Stekelenburg | timeline score: 7 | |
| Jan 26, 2018 at 22:30 | comment | added | Dan Piponi | In particular, the "multiplication" is exactly what you might guess: it maps a bag of bags of things to a bag of things by dissolving the inner bags leaving all their contents in the outer bag. | |
| Jan 26, 2018 at 22:01 | history | edited | Ben Sprott | CC BY-SA 3.0 |
deleted 22 characters in body
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| Jan 26, 2018 at 18:51 | history | edited | Ben Sprott | CC BY-SA 3.0 |
added 130 characters in body
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| Jan 26, 2018 at 17:01 | review | Close votes | |||
| Jan 29, 2018 at 17:03 | |||||
| Jan 26, 2018 at 16:00 | comment | added | Mike Shulman | FWIW, not all data structures are monads. | |
| Jan 26, 2018 at 15:24 | comment | added | Ben Sprott | I believe a monoid on X would give lists. A monoid element has a notion of order of elements in a product (ie a word). A bag has no notion of that.But, yes a set with finite multiplicities would be a bag, I think. So I am not sure my thought about monoids is correct. Oh, Commutative monoids, so that every word is actually an equivalence class of all permutations, so order is forgotten. | |
| Jan 26, 2018 at 15:21 | comment | added | Tom Leinster | You might get better answers if you give a mathematical definition of bag. My possibly incorrect memory is that a bag is a set with finite multiplicities. In that case, given a set $X$, a bag with elements in $X$ is precisely an element of the free commutative monoid on $X$. So, bags are generated by the free commutative monoid monad. But I don't know whether that answers your question. | |
| Jan 26, 2018 at 15:01 | history | edited | Martin Sleziak |
added (monads) tag - if I missed something and it is not actually relevant to the question, feel free to revert my edit
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| Jan 26, 2018 at 14:56 | history | asked | Ben Sprott | CC BY-SA 3.0 |