Timeline for Are there categories whose internal hom is somewhat 'exotic'?
Current License: CC BY-SA 4.0
8 events
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| Aug 19, 2019 at 15:58 | history | edited | David White | CC BY-SA 4.0 |
Fixed spelling and minor typos
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| Aug 19, 2019 at 8:40 | comment | added | Derek Elkins left SE | Just to explicitly connect some of the examples, the "free suplattice" view can be viewed as a decategorification of the fact the category of presheaves on a (small) category can be viewed as its free cocompletion. We then have that a profunctor $\mathcal C\times\mathcal D^{op}\to\mathbf{Set}$ is the same thing as a functor $\mathcal C\to[\mathcal D^{op},\mathbf{Set}]$ which is the same thing as a cocontinuous functor $[\mathcal C^{op},\mathbf{Set}]\to[\mathcal D^{op},\mathbf{Set}]$ which decategorifies into a suplattice morphism. | |
| Aug 18, 2019 at 22:26 | history | edited | Simon Henry | CC BY-SA 4.0 |
edited body
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| Aug 18, 2019 at 20:05 | comment | added | Simon Henry | Yes absolutely. | |
| Aug 18, 2019 at 19:50 | comment | added | seldon | Also the last part of very insightful, I love it. Thanks again! | |
| Aug 18, 2019 at 19:44 | comment | added | seldon | This is really a great example, thank you! Just to clarify: the external hom here is the power set of $X \times Y$, while the internal hom is just $X \times Y$ right? It is very dramatic, maybe the most striking here because of its simplicity. | |
| Aug 18, 2019 at 18:46 | history | edited | Simon Henry | CC BY-SA 4.0 |
added 1417 characters in body
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| Aug 18, 2019 at 18:38 | history | answered | Simon Henry | CC BY-SA 4.0 |