Timeline for Any example of a non-strong monad?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 6, 2022 at 17:31 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https
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| Aug 18, 2015 at 3:34 | comment | added | Vlad Patryshev | Exception monad has as many enrichments as there are semigroups defined on a given object. | |
| Dec 12, 2012 at 15:58 | comment | added | Ohad | As Tom believes above, there is a monad with two different enrichments. See Example 4.1 in John Power's ["Unicity of enrichment over Cat or Gpd"][1] which John Bourke mentions above. [1]:opus.bath.ac.uk/23104 | |
| Jan 23, 2012 at 15:05 | comment | added | John Bourke | Here is a very simple example of the same kind suggested by Finn and due to John Power: it is a monad on Cat which cannot be extended to a 2-monad and therefore cannot have a strength. It is the monad T on Cat whose algebras are categories C equipped with a endofunction on the set of objects ob(C) of C. It has value $TC= C + (N \times ob(C))$ where $N$ is the discrete category with set of objects the natural numbers. For the details of why it cannot be extended, see Example 3.1 of Power's "Unicity of enrichment over Cat or Gpd" freely available at opus.bath.ac.uk/23104 | |
| Jan 13, 2012 at 7:16 | vote | accept | Vlad Patryshev | ||
| Jan 11, 2012 at 21:27 | history | answered | Finn Lawler | CC BY-SA 3.0 |