* Reference wanted
@ 2003-01-08 22:52 Oswald Wyler
0 siblings, 0 replies; 2+ messages in thread
From: Oswald Wyler @ 2003-01-08 22:52 UTC (permalink / raw)
To: categories
For a category E with finite limits, every morphism f:A\to B induces a
pullback functor f^*:E/B\to E/A of slice categories, with a left adjoint
given by u:a\to a' \mapsto u:fa\to fa'. It has been well known since the
late 1960's that this left adjoint is comonadic, but who proved this,
and where?
^ permalink raw reply [flat|nested] 2+ messages in thread
* Reference wanted
@ 2001-12-06 14:00 Oswald Wyler
0 siblings, 0 replies; 2+ messages in thread
From: Oswald Wyler @ 2001-12-06 14:00 UTC (permalink / raw)
To: categories
I'm sure that the following is known, but I've never seen it in print.
Does someone have a reference for it?
Proposition. Let U be a monadic functor, in the sense of Mac Lane's CWM.
If U factors U=HG with H faithful and amnestic, and G having a left adjoint,
then G is monadic.
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