Timeline for Retractions of Yoneda are reflectors, i.e., left adjoints?
Current License: CC BY-SA 3.0
8 events
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| Aug 29, 2019 at 19:12 | comment | added | Todd Trimble | @IvanDiLiberti Sorry for the delay. It's Anders Kock's paper on when multiplication structures are left adjoint to units (aka KZ monads): Journal of Pure and Applied Algebra 104 (1995), 41-59. | |
| Aug 27, 2019 at 5:29 | comment | added | Ivan Di Liberti | What is the title of this paper by Kock? The link seems to be corrupted. | |
| Apr 19, 2017 at 10:37 | history | edited | Todd Trimble | CC BY-SA 3.0 |
title: retractors --> reflectors
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| Jan 9, 2015 at 12:25 | comment | added | john | In fact Prop 3 on Street's paper mentioned implies that idempotents split in $C$. Combining this with what Mike says should consequently ensure that $y_{c}$ always has a left adjoint, although perhaps you have to change $s$ itself? | |
| Dec 31, 2014 at 6:02 | comment | added | Mike Shulman | Just to have it recorded here, Theorem 3.5 of Kock's paper (and its proof) says that if there is a retraction, then there is a left adjoint obtained by splitting an idempotent of the retraction functor. So the question is whether that idempotent can be nontrivial. | |
| Dec 29, 2014 at 13:51 | comment | added | Todd Trimble | @john Thank you! I knew of Kock's paper, but that result I hadn't picked up before. That's helpful. | |
| Dec 29, 2014 at 10:54 | comment | added | john |
Just a very quick comment. If idempotents split in C then I would hazard a guess that s must be left adjoint - else not. Theorem 3.5 of http://home.math.au.dk/kock/msau.PDF" and the discussion above it may be relevant, as may be the note Consequences of splitting idempotents" off Ross Street's webpage.
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| Dec 29, 2014 at 2:19 | history | asked | Todd Trimble | CC BY-SA 3.0 |