Subject: categories: Finitely presentable presheaves

From: [email-masked] (Marco Grandis)
Date: Tue, 16 May 2000 16:55:28 +0100

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: [email-masked]
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