Yes - Fred - that's correct, the question is about the algebras of the double power locale triple (so, over locales and not set). However - Michael - if somehow the example on p72 is applicable in this case (I cannot see how it can be), do please let me know, as I would be very pleased if the question is settled. Thanks, Christopher -----Original Message----- From: Fred E.J. Linton [mailto:fejlinton@usa.net] Sent: 27 March 2015 16:31 To: Michael Barr; Categories mailing list Subject: categories: Re: coequalizers in the category of algebras for the double powerset triple If I had thought Richard's monad was on the category of sets, I'd have answered the same way: | From: Michael Barr <barr@math.mcgill.ca> | | > Recently there was a question as to whether these coequalizers exist. | > Unless I have misunderstood the question, the affirmative answer is | > given | > in the example in the middle of p.72 of Linton's paper in TAC | > reprint #18. But Richard writes of his monad as being "on the category of locales", and there I'm not so sure ... . Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ] _______________________________________________________________________ This email is intended only for the use of the individual(s) to whom it is addressed and may be privileged and confidential. Unauthorised use or disclosure is prohibited. If you receive this e-mail in error, please advise immediately and delete the original message without copying, using, or telling anyone about its contents. This message may have been altered without your or our knowledge and the sender does not accept any liability for any errors or omissions in the message. This message does not create or change any contract. Royal Bank of Canada and its subsidiaries accept no responsibility for damage caused by any viruses contained in this email or its attachments. Emails may be monitored. RBC Capital Markets is a business name used by branches and subsidiaries of Royal Bank of Canada, including Royal Bank of Canada, London branch and RBC Europe Limited. In accordance with English law requirements, details regarding RBC Europe Limited and Royal Bank of Canada, London Branch are set out below: RBC EUROPE LIMITED Registered in England and Wales 995939 Registered Address: Riverbank House, 2 Swan Lane, London, EC4R 3BF. Authorised by the Prudential Regulation Authority and regulated by the Financial Conduct Authority and the Prudential Regulation Authority. ROYAL BANK OF CANADA, LONDON BRANCH Incorporated in Canada in 1869 with Limited Liability. Registered in England and Wales BR000548 Registered Address: 1 Place Ville Marie, Canada. Branch location: Riverbank House, 2 Swan Lane, London, EC4R 3BF. Authorised and regulated by the Office of the Superintendent of Financial Institutions of Canada. Authorised by the Prudential Regulation Authority. Subject to regulation by the Financial Conduct Authority and limited regulation by the Prudential Regulation Authority. Details of our regulation by the Prudential Regulation Authority are available from us on request. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]