Timeline for What functors between categories of algebras are induced by morphisms of monads on $\mathrm{Set}$?
Current License: CC BY-SA 4.0
9 events
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| Jun 10, 2023 at 7:05 | history | edited | varkor | CC BY-SA 4.0 |
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| Jun 9, 2023 at 5:33 | comment | added | varkor | @ArshakAivazian: yes, I should have mentioned that this doesn't just work for Set (Frei works with monads on an arbitrary base category, for instance). Glad I could help :) | |
| Jun 9, 2023 at 5:30 | history | edited | varkor | CC BY-SA 4.0 |
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| Jun 8, 2023 at 22:35 | comment | added | Arshak Aivazian | I have now found that the same is true for an arbitrary category $C$ ($\mathrm{Set}$ is not essential here). See Francis Borceux - Handbook of categorical algebra II, Prop 4.5.9. | |
| Jun 8, 2023 at 21:41 | vote | accept | Arshak Aivazian | ||
| Jun 8, 2023 at 21:41 | comment | added | Arshak Aivazian | The fact is that I expected at least such functor properties as right adjoint, rank and wanted to know the full list. But it turned out that everything is so simple. Thanks again! | |
| Jun 8, 2023 at 21:39 | comment | added | Arshak Aivazian | Thanks a lot! Moreover, all such functors automatically have rank $\lambda$ (because their composition with a forgetful functor (which has rank $\lambda$ and is conservative) is a functor of rank $\lambda$) and preserve all limits (for a similar reason), hence are right adjoint functors. | |
| Jun 8, 2023 at 21:27 | history | edited | varkor | CC BY-SA 4.0 |
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| Jun 8, 2023 at 21:15 | history | answered | varkor | CC BY-SA 4.0 |