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2012.117: Sheaves as essentially algebraic objects

2012.117: Philip Bridge (2012) Sheaves as essentially algebraic objects.

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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 2000 > 16 Associative rings and algebras
MSC 2000 > 18 Category theory; homological algebra
MIMS number:2012.117
Deposited By:Mr Philip Bridge
Deposited On:14 December 2012

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