Timeline for a category associated with an inverse semigroup
Current License: CC BY-SA 3.0
3 events
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| Mar 15, 2018 at 23:10 | comment | added | David Hillman | Thanks for that. I would add though that beauty is in the eye of the beholder! For instance, I like $C$ because we have inverse acting as a period-2 contravariant functor from $C$ to itself. Namely: if $e\colon a\to b$ (because $e=aa^{-1}eb^{-1}b$) then also $e^{-1}\colon b^{-1}\to a^{-1}$ (because $e^{-1}=b^{-1}be^{-1}aa^{-1}$). | |
| Mar 15, 2018 at 12:55 | comment | added | Benjamin Steinberg | This is connected to why the category is equivalent to the Karoubi envelope in the regular case but you can't get to ordinary composition in the non-regular case where the automorphism groups are the classical Schutzenberger groups, whence the name, which don't necessarily embed in the semigroup. | |
| Mar 15, 2018 at 8:17 | history | answered | hänsel | CC BY-SA 3.0 |