631:)Â :). So i do not think that a simple or one-sided relation between usual monoids and monoidal categories (like "objects in a strict monoidal category form a monoid") would be a complete justification of the name, despite what Mac Lane writes. I think that notions of a monoid and a monoidal category are complementary: monoidal categories allow to generalize the notion of a usual monoid, and with this more general definition they become monoids themselves in the monoidal category of categories and functors. (Of course one needs to be careful and talk about the category of "small" categories, etc.). --
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double-dutch for all the purpose they would serve. (Do we have a little template thingy that says "Definition needed" like the "citation needed" one?) I have been banging on for some time about the need to be both precise and clear and suitable for the intended audience, the latter not being professional mathematicians, logicans, or philosophers. You then are the best judge of that. If you look at my discussion page, I have a message from a reader who said how clear and helful were the logic articles she had read. That is praise indeed, and more liek that are sought.--Philogo 13:40, 8 May 2008 (UTC)
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able to map it out and have some understanding. The goal of these editors seems to be that it will only be useful and understandable to mathematicians. So can you see why I would be very upset over all of this. I think you need to think about the needs of the whole community over the very limited interests of the math department.
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precision, and the third sentence names the result as 'composite function'. They increase (mildly) in technicality. They usually do it that way in
Knowledge. It is a deliberate choice. Your new version of the first sentence is now defining the noun. If it shall stay that way, the following sentences must be adjusted accordingly.
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on a single page within a 24-hour period. Undoing another editor's workâwhether in whole or in part, whether involving the same or different material each timeâcounts as a revert. Also keep in mind that while violating the three-revert rule often leads to a block, you can still be blocked for edit
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A declassified memo exists that informed LBJ on the Monday following the assassination that he had to "convince the people LHO did it and did it alone" and that he was to form a "commission" to appear official avoid prying eyes from
Congress or other gov bodies who'd want serious answers and fact. I
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Okay, lets take it easy on each other. My goal in creating that article was to cover the concept of "one person has a different interpretation of things than another" Here I am thinking that people of all kinds might be able to benefit from it. Maybe two regular people having a disagreement could be
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I mentioned informal as a description of the style in which it was written before. Style which my edit tried to keep. I am not implying that it strictly has to be that way. What is awkward now is the repetition occurring between the first and second sentence. They are saying the same thing. So, one
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Well, but all of them should be correct and comprehencible anyway, maybe some less precise than the others. My first sentence does not use any technical notation or language, not even domain and range specification, but anything would be fine with me, as long as it is correct (and comprehensible).
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For me, that all amounts to roughly the same reason. It seems obvious that monoid objects are called so just because in the monoidal category of sets they are the usual monoids. And monoidal categories are a generalisation of strict monoidal categories. Saying that the latter are the monoid objects
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most about is that the information be correct and comprehensible, whether the style is formal or informal, and whether there is any redundancy or not. Currently, I would prefer to leave it to the others to decide how to deal with it (as long as any misleading or inaccurate statements are avoided).
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You haven't told the lay reader who finds this article whether this is supposed to be about, e.g. the building of houses ("structures"), organizations (a church council or a commercial firm is a "structure"), etc. That this is supposed to be about mathematical logic needs to be said in a way that
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Personally, I see no reason to write a paragraph where one sentence would suffice, so shrinking the whole introduction into a one-sentence informal (by mathematical standards) definition would look the most natural to me. However, I am afraid that the others won't agree. Anyway, what i care the
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Hi, thanks for the message. I do not have time or desire to follow this issue too closely, maybe i will be just looking to the talk page from time to time. I am trying to use common sense and logic to prevent publishing beliefs worded as facts in
Knowledge. The best thing i've come up with is to
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The condition is stronger than that, because the "multiplication" also acts on arrows, and is a bifunctor. Mac Lane writes that they are called monoidal because the bifunctor is associative. It is not clear to me if this reason it the official one, but there seem to be a good reason. For example,
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Note that there is now repetition in the second sentence of the same content that you added in the first sentence. Also take into account that 'function composition' can be both a noun and a verb. Before, the sentence was explaining the verb in simple words, then the second sentence in full
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The article and other under the logic banner will be sucessful for the intended audience, therefore, if you for instance come to understand the terms you mentione and any other used in the article(s). If you do not unerstand the terms used then we might just as well write the articles in
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I know I'm terrible! Can it. I tell you what Hans, I think you are all right in general, but I don't like your style. Furthermore, you and the other mathematicians seem determined to close your minds to covering even the most basic philosophical background for these concepts. That's what
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1295:; that means that you are repeatedly changing content back to how you think it should be, when you have seen that other editors disagree. To resolve the content dispute, please do not revert or change the edits of others when you are reverted. Instead of reverting, please use the
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Hi, I have undone a change you have made to that article. Please comment if you disagree. Also, what do you mean by âusual monoids are exactly the monoids in the monoidal category of sets with
Cartesian productâ? What are âthe monoidsâ in a monoidal category? Best regards
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page, I don't know if this was one of your changes, but I assume you must be familiar with the subject. I believe the 6th step of the
Algorithm has a typo, but since it would change the algorithm's function I was hoping to get a second opinion. I have noted it on
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philosophers call being anti-intellectual and unreflective. If you don't understand something intellectually, you don't understand it AT ALL. At least I am capable of deferring to experts in their own areas. I've been patient with you guys up to now. Step off.
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I recently contributed a carefully worded reference to the this issue that was immediately reverted by admin. I reverted it back, not knowing that move would earn me the honor of starting "engaging in a revert war", which clearly was not my intention.
484::) ), and it seems that this is the kind of logic the article/lede is currently about. I also understand the phrase "common-sense logic". The phrase "philosophical logic" evokes some associations, but nothing clear. I will try to be useful however. --
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574:, which satisfy the usual laws for the usual monoids, but expressed purely in terms of arrows. What do you think about this as a reason to call the category monoidal? I do not know the true historical explanation of the name --
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at what point? If the first function is from reals to reals, its application can only produce a real, not another function, etc. I do not see a point to not define something directly in the first sentence if you easily can.
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What can be said in defence of the current situation, is that the second sentence is more detailed and formal than the first one, and it uses the technical notation for function's domain and codomain. --
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I totally agree with what you've written. The facts are truly there, but they are "inconvenient" facts and stray from the urban myth which is the parroting of gov provided untruths. What can we do?
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in the monoidal category of categories is, when taking the motivation for the term âmonoid objectâ into account, about the same as saying that their objects form a monoid, with morphism filled in
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I am very glad to see that we have a new active model theory editor. I am sorry that you have run into
Gregbard with your first mathematical article â but then, this kind of encounter adds the
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How about something along the lines of: "function composition is an operation that takes two functions and produces a new one by connecting the input of one to the output of the other"? --
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Interesting, thanks for the clarification. I was assuming that they are called monoidal categories because, well, the objects of a strict monoidal category actually form a monoid ⌠â
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too.) I will respond here to one of the questions/assertions you made elsewhere, and hope that you will be able to answer the others yourself. Here we go: I did not try to
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is, and i am familiar with some basics of it. I can think of a few non-mathematical interpretations of Mathematical Logic (yet another meaning of
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and make any comments at new section at end of 50 pages of discussion. Bless,--Philogo 00:28, 8 May 2008 (UTC)--Philogo 00:29, 8 May 2008 (UTC)
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or using four tildes (~~~~); this will automatically produce your username and the date. Also, please do your best to always fill in the
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Thanks. I understand. I found the official memo and source and have inserted the info which is not "belief", but rather fact.
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You are absolutely right, can you do it for me, please? :) The only thing i can say in my defence is that i did link the word
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I agree with the change, i think i was trying to explain what a "natural isomorphism" is, but this is a bit off topic. --
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make a reference request at least. It is not possible to argue with anything when the person you talk to cites
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is not comprehensible even for a mathematician (assuming he does not know already what is being defined). The
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function composition is the application of one function to the result of another to produce a third function
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for how this is done. If discussions reach an impasse, you can then post a request for help at a relevant
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monoidal category, that is the natural isomorphisms in the definition are identities. Then a monoid in
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Hello Quilbert, I am following "Categories for Working Mathematician" by Saunders Mac Lane. Let
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is. I am only somewhat familiar with common layman usage of these words. I only know what
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with the "general" definition of a monoid (in a monoidal category), the
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956:: Voting now open!
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1884:voting page
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1351:Jasper Deng
1309:noticeboard
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409:beat you up
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882:Thanks. --
803:changing â
700:Mediation?
474:Philosophy
405:Hans Adler
361:Hans Adler
307:signatures
264:structures
194:Help pages
184:Cheatsheet
1864:site bans
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1301:consensus
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797:your edit
333:structure
232:Practice
1362:Lead of
1337:warringâ
1311:or seek
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865:I edited
777:contribs
765:unsigned
664:Quilbert
594:Quilbert
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234:civility
1891:NoACEMM
1803:NoACEMM
1713:NoACEMM
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1334:reverts
1117:Botlord
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686:Cokaban
633:Cokaban
621:monoids
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226:Follow
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1354:(talk)
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910:. The
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544:strict
399:Hello
357:MMORPG
769:4eyes
744:WP:RS
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470:Logic
351:Hello
68:Tucky
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904:Hi,
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