Question about coequalizers in the category of algebras of the double power locale monad

Question about coequalizers in the category of algebras of the double power locale monad

[Townsend, Christopher]

Hello - 

I was wondering if anyone knew whether or not the category of algebras of the double power locale monad has coequalizers? Reflexive ones will do. 

Thanks, Christopher 


From: Townsend, Christopher <Christopher.Townsend <at> rbccm.com>
Subject: RE: Colimits in the category of algebras of power locale monads
Newsgroups: gmane.science.mathematics.categories
Date: 2013-12-30 16:46:31 GMT (1 year, 11 weeks, 6 days, 12 hours and 54 minutes ago)

Hello, 

If P is the upper, lower or double power locale monad on the category of locales (Loc), does anyone know if the
corresponding category of EM algebras,  Loc^P, has (i) coequalizers; and/or, (ii) finitary coproducts? 

Thanks, Christopher  

info <at> christophertownsend.org

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Re: Question about coequalizers in the category of algebras of the double power locale monad

[Paul Taylor]

Chris Townsend asked the same question,

> I was wondering if anyone knew whether or not the category of algebras
> of the double power locale monad has coequalizers? Reflexive ones will do.

more than a year ago on MathOverflow,

mathoverflow.net/questions/154883/coequalizers-in-the-category-of-algebras-of-the-double-power-locale-monad

where I gave as much of an answer as I could.

Nobody else responded there and I suspect that
no more is known about this topic now.

But if anyone does know any more, I suggest that
they take advantage of the formatting facilities
of MathOverflow and also keep things in one place.

Paul Taylor.


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