Timeline for Projective resolutions for commutative monoids
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 2, 2016 at 12:56 | comment | added | Hannes Thiel | @YemonChoi I think Mon is not semi-abelian. I think it is regular and exact (in the sense of Barr), but I think it is not protomodular. A problem (for me) is that such concrete statements are difficult to find in the literature. | |
| Mar 2, 2016 at 11:53 | comment | added | Yemon Choi | I suspect that Mon is also what Borceux, Bourn and others call a "semi-abelian category", which is roughly speaking a category that has many of the good properties of abelian categories (mono and epi implies iso) but is not additive. So one may also be able to use their machinery to define and study derived functors, however I don't remember right now what exactly they do | |
| Mar 2, 2016 at 11:49 | comment | added | Yemon Choi | While the links given by Vladimir Dotsenko are probably more useful, it is worth noting that you can certainly get a "bar resolution" from general machinery (going back to categorists in the 1960s I think). The general machinery applies whenever you have a pair of adjoint functors, and allows you to build a "simplicial object" which is some kind of "free resolution". Look in Chapter 8 of Weibel's book, for instance. Here we'd look at the forgetful functor U from Mon to Set and its left adjoint F (the free commutative monoid functor). | |
| Mar 2, 2016 at 11:19 | answer | added | Vladimir Dotsenko | timeline score: 5 | |
| Mar 2, 2016 at 11:00 | history | asked | Hannes Thiel | CC BY-SA 3.0 |