Timeline for Transporting algebraic structure along adjoint equivalences
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 3, 2014 at 7:54 | comment | added | john | That coherent 2-groups are the algebras for a flexible 2-monad on groupoids is not hard to see using presentations of 2-monads - it can be built as a flexible (indeed pie) colimit of free 2-monads on signatures. | |
| Apr 3, 2014 at 7:51 | comment | added | john | Amongst the properties mentioned by Chris above, the only one that may fail for the strict algebras of a 2-monad is the ability to transport structure along equivalences. He mentioned flexible 2-monads: for a flexible 2-monad each pseudoalgebra is isomorphic to a strict algebra, with the same underlying object. Since one can transport pseudoalgebra structure along equivalences in general, the same holds for strict algebras for flexible 2-monads. This is discussed in "Monoidal functors generated by adjunctions..." by Kelly and Lack, for instance. | |
| Apr 2, 2014 at 1:41 | vote | accept | David Roberts♦ | ||
| Apr 2, 2014 at 1:41 | comment | added | David Roberts♦ | Ah, excellent. Thank you, and apologies for the slightly grumpy tone of my other comments! | |
| Apr 1, 2014 at 23:05 | history | edited | Chris Schommer-Pries | CC BY-SA 3.0 |
one word.
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| Apr 1, 2014 at 22:24 | history | answered | Chris Schommer-Pries | CC BY-SA 3.0 |