Timeline for Externalising monoids using the Yoneda-embedding and relation to Kleisli categories
Current License: CC BY-SA 3.0
4 events
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| Jul 31, 2012 at 10:02 | comment | added | Zhen Lin | I was deliberately imprecise. A more accurate version would be to say that the external monoid $\mathcal{C}(I, M)$ acts on $M$ by the given formula – which can be regarded as the formula for the left self-action of $M$ "parametrised" by $I$. Alternatively, with more assumptions on $\mathcal{C}$ one can use a more elegant construction as in Michal's answer – what is happening belongs more in the realm of enriched category theory. | |
| Jul 31, 2012 at 9:27 | comment | added | user11863 | Thank you for your answer. I will take time to go through it in detail. Could you please clarify the answer you gave about step 2? I was considering this, by turning the set $\mathcal{C}(I,X)$ into a category with one object and using the Yoneda-embedding, but that gives a monoid on $\mathcal{Set}(\mathcal{C}(I,X),\mathcal{C}(I,X))$ rather than $\mathcal{C}(X,X)$. Can this be fixed? | |
| Jul 31, 2012 at 0:41 | history | edited | Zhen Lin | CC BY-SA 3.0 |
added 220 characters in body
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| Jul 30, 2012 at 16:37 | history | answered | Zhen Lin | CC BY-SA 3.0 |