Timeline for Is there a general notion of semigroup action?
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8 events
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| Sep 1, 2014 at 10:04 | comment | added | Thomas Klimpel | @AndrejBauer Your initial suggestion to take an inverse semigroup and a semigroup homomorphism into $\operatorname{Hom(X,X)}$ (for an object $X$ from a suitable category $\mathcal C$) still seems the most promising route to me now. If I take a category of partial injections for this, then I get at least the intended representation theorem. But what I don't like about this is that the inverse semigroup itself can't live inside a category of partial injections. | |
| Sep 1, 2014 at 7:44 | comment | added | Andrej Bauer | Your semigroup and the object live in the same category. Another option is to let semigroup live in the category of sets (or wherever your hom-sets live) and then you can define what it means for such a semigroup to act on an object in a category. | |
| Aug 31, 2014 at 23:28 | comment | added | Thomas Klimpel | @BenjaminSteinberg I will read the three papers by Cockett and Lack on restriction categories. But I started by trying to make sense of the comments closer to my comfort zone. For example: "The idempotent splitting of an inverse semigroup is not a groupoid." now makes more sense for me, because the idempotents of an inverse semigroup form a semilattice, but a semilattice is not a groupoid. Or I verified that "define partial maps ... as certain spans" is essentially the "... construction based on subobjects, equivalence classes and pullbacks ..." found in some category theory texts. | |
| Aug 31, 2014 at 22:57 | history | edited | Thomas Klimpel | CC BY-SA 3.0 |
extended the answer, as previously indicated
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| Aug 31, 2014 at 22:52 | history | edited | Thomas Klimpel | CC BY-SA 3.0 |
extended the answer, as previously indicated
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| Aug 31, 2014 at 15:04 | comment | added | Benjamin Steinberg | You should look at the restriction category stuff. It axiomatizes the domain and range idempotents. | |
| S Aug 31, 2014 at 13:24 | history | answered | Thomas Klimpel | CC BY-SA 3.0 | |
| S Aug 31, 2014 at 13:24 | history | made wiki | Post Made Community Wiki by Thomas Klimpel |