Sheaves as essentially algebraic objects

Bridge, Philip (2012) Sheaves as essentially algebraic objects. [MIMS Preprint]

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Abstract

We develop the notion of essentially algebraic theories from [1]. We associate with each Grothendieck site a corresponding essentially algebraic theory whose models are the sheaves on that site. This is used to classify locally finitely presented toposes, and to show that the category of modules over a ring object in a locally finitely presented topos is also locally finitely presentable.

Item Type:	MIMS Preprint
Uncontrolled Keywords:	ringed space, sheaf, module, category, locally finitely presented, locally finitely generated
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 16 Associative rings and algebras MSC 2010, the AMS's Mathematics Subject Classification > 18 Category theory; homological algebra
Depositing User:	Mr Philip Bridge
Date Deposited:	14 Dec 2012
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1932

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