Re: Further to my question on adjoints

[Eduardo Dubuc <edubuc@dm.uba.ar>]

Consider the dual finitary question: In universal algebra in order to show
that finitely presented objects  are closed under coequalizers it is
essential  that a amorphism of finitely presented objects lift to a
morphism  between the free. Is this the only way to prove it ? :

" but when I look at examples, it has turned out to be true
 for other reasons."

greetings  e.d.


>
> In March I asked a question on adjoints, to which I have received no
> correct response.  Rather than ask it again, I will pose what seems to be
> a simpler and maybe more manageable question.  Suppose C is a complete
> category and E is an object.  Form the full subcategory of C whose objects
> are equalizers of two arrows between powers of E.  Is that category closed
> in C under equalizers?  (Not, to be clear, the somewhat different question
> whether it is internally complete.)
>
> In that form, it seems almost impossible to believe that it is, but it is
> surprisingly hard to find an example.  When E is injective, the result is
> relatively easy, but when I look at examples, it has turned out to be true
> for other reasons.  Probably there is someone out there who already knows
> an example.
>
> Michael
>
>