Timeline for Does the Eilenberg Moore Construction Preserve fibrations?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 4, 2019 at 15:30 | vote | accept | Max New | ||
| Jan 4, 2019 at 15:17 | history | edited | Tim Campion | CC BY-SA 4.0 |
added 50 characters in body
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| Jan 4, 2019 at 15:16 | comment | added | Tim Campion | Oh wow! Yes, thanks for catching that! | |
| Jan 2, 2019 at 20:46 | comment | added | Max New | When you say the forgetful functor $Mnd(C) \to C$ do you mean the inclusion $C \to Mnd(C)$ that picks the identity monad instead? That's what it looks like it says in Street. | |
| Dec 30, 2018 at 15:42 | comment | added | Mike Shulman | I think it would probably be easier to understand fibrations in Mnd(C) using the characterization of fibrations in terms of limits. Since the forgetful functor $\mathit{Mnd}(C)\to C$ also preserves limits (when C has Kleisli objects it has a left adjoint), being a fibration in Mnd(C) just means being a fibration in C together with the extra structure that the universal lift-assigning functor and transformation lift to Mnd(C). Then just work out what that means explicitly. | |
| Dec 30, 2018 at 15:00 | comment | added | Tim Campion | Fibrations can be detected by homming in, so one answer will probably be a tautological one: $p: E \to B$ is a fibration if $Mnd(C)(X,E) \to Mnd(C)(X,B)$ is a fibration for all monads $X$, which will probably reduce in the case $C = Cat$ to the induced map of Eilenberg-Moore objects being a fibration. | |
| Dec 29, 2018 at 16:37 | comment | added | Max New | So just need to figure out what a fibration object in Mnd is then. | |
| Dec 29, 2018 at 5:50 | history | answered | Tim Campion | CC BY-SA 4.0 |