17 May
2000
17 May
'00
1:55 a.m.
Consider the category of presheaves C^ on a small category, C. Plainly, a finite colimit F of representables presheaves is finitely presentable, in the usual sense: C^(F, -) preserves filtered colimits. But the converse is also true and seemingly well known: every finitely presentable presheaf is a finite colimit of representables. Is this proved somewhere? Best regards Marco Grandis Dipartimento di Matematica Universita' di Genova via Dodecaneso 35 16146 GENOVA, Italy e-mail: grandis@dima.unige.it tel: +39.010.353 6805 fax: +39.010.353 6752 http://www.dima.unige.it/STAFF/GRANDIS/ ftp://pitagora.dima.unige.it/WWW/FTP/GRANDIS/