Timeline for On the notion of partial semigroup
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Mar 6, 2013 at 19:31 | comment | added | Salvo Tringali | @Gerhard. No worries! Instead, thank you for sharing your reflections on this. | |
| Mar 6, 2013 at 18:24 | comment | added | Gerhard Paseman | By the way, for me a partial semigroup is equivalent to a fragment of its multiplication table, where it is possible to complete it to be the table of an associative operation. Gerhard "And What About Impartial Semigroups" Paseman, 2013.03.05 | |
| Mar 6, 2013 at 18:17 | comment | added | Gerhard Paseman | The only other take I have on your question I parody as "Universal Algebraists cross themselves from right to left, while Category Theorists do down to up; is there a higher rationale which indicates which is better or more natural?" . I intend no disrespect; it's just that without application, I see the question as worse than silly, I see it as pointless. With application, I see a point to the question,and I stand by my previous responses. Please consider this as explaining my shortcomings, not as criticizing your question or motives. Gerhard "Ask Me About System Design" Paseman, 2013.03.05 | |
| Mar 6, 2013 at 18:08 | comment | added | Gerhard Paseman | I don't see how to accomplish A and B in the same context, where A is "putting aside any and all applications of the objects and definitions", and where B is answering your question, which I rephrase as "what is the most natural way, determined by higher principles, to apply the term partial semigroup? ". Whichever way you do B, you will have to consider how to use the result, which to me speaks of application. (Continued) Gerhard "What Is Math Without Application?" Paseman, 2013.03.05 | |
| Mar 6, 2013 at 9:51 | comment | added | Salvo Tringali | (...) This is, of course, unquestionable, and it reflects Andreas & Gerhard's position. Yet, what I'm barely trying to say is that, if we put applications to the side for one moment, we face the fact that there's a higher rationale providing an abstract notion of subobject, which is telling us that, from a conceptual point of view, Grätzer's notion of relative subalg should be privileged, & I'd like to find, if possible, a similar motivation for the notion of partial sgrp. But again, this is just what it is, namely abstract nonsense, and it has little to do here with the everyday practice. | |
| Mar 6, 2013 at 9:23 | comment | added | Salvo Tringali | For the record, Evseev's notion of subgrpd is essentially an instance of the more general notion of (partial) subalgebra given by Grätzer at p. 80 of his Universal Algebra (2nd ed., 2008). The notion implied by the categorial point of view is, instead, the one of relative subalgebra, which Grätzer himself introduces a few lines after. To quote him, "In many papers, the authors select one of each [...] and give the reasons for their choice. In the author's opinion, all these concepts have their meirts and drawbacks, and each particular situation determines which one should be used." (...) | |
| Mar 5, 2013 at 16:21 | comment | added | Salvo Tringali | [...] the notion of subobject that is "naturally" implied by looking at the question from the "privileged" perspective of categories. Do you/anybody know if this has been "corrected" in the book? | |
| Mar 5, 2013 at 16:08 | comment | added | Salvo Tringali | @Boris. Thanks, but I may have problems in finding a copy of the book that you mention as a last entry in your list. Yet, I see from the 1988 English translation of Evseev's survey that he's using the term groupoid in the sense of Bourbaki's magma. That's fine, but I find the definition of a subgroupoid provided in the paper unconceivable from any conceptual point of view: Evseev lets a submagma of a magma $\mathbb M=(M,\star)$ be a subset $N$ of $M$ s.t. $a\star b\in N$ for all $a,b\in N$ s.t. $a\star b$ is defined in $\mathbb M$. In my view, this is "wrong", for it doesn't agree with [...] | |
| Mar 5, 2013 at 15:35 | comment | added | Boris Novikov | @Salvo Tringali: Maybe. As I knew Lyapin, he was a great "conceptualist" in Semigroups. | |
| Mar 5, 2013 at 15:31 | comment | added | Boris Novikov | @Victor :Sorry, I do not quite understand your question :-( | |
| Mar 5, 2013 at 14:44 | comment | added | Salvo Tringali | Many thanks for the references. I will look at the papers tomorrow, but I don't think that the authors give any conceptual motivation to support their own definitions, right? | |
| Mar 5, 2013 at 14:36 | comment | added | Victor | Boris, can you do homological stuff on partial grupoids? | |
| Mar 5, 2013 at 13:49 | history | answered | Boris Novikov | CC BY-SA 3.0 |