To Thomas and Richard, I have a question regarding certain finite limit preserving functors Set-->Set. If L is a locale, then the functor Hom(L,-):Set-->Set preserves finite limits, where Hom(L,X) denotes the set of morphisms of locales L-->X for a discrete locale X. Is there is a simple characterization of these flp functors? Best, André ________________________________________ From: Thomas Streicher [streicher@mathematik.tu-darmstadt.de] Sent: Tuesday, October 23, 2018 4:56 AM To: Richard Garner Cc: categories@mta.ca Subject: categories: Re: characterization of flp endofucntors on Set? Dear Richard, thanks for your answer. Offline I have received a reply by Jonas Frey which answers my question satisfactorily. Let U be a Groth. universe then Lex(U,Set) consists of filtered/directed colimits of representables. Accordingly, Lex(U,U) is equivalent to the full subcat of Set^U on U-small directed colimits of representables. But that sounds related to what Blass says, isn't it. Best, Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]