论文信息 - Applications of Sup-Lattice Enriched Category Theory to Sheaf Theory

Applications of Sup-Lattice Enriched Category Theory to Sheaf Theory

Grothendieck toposes are studied via the process of taking the associated Sl-enriched category of relations. It is shown that this process is adjoint to that of taking the topos of sheaves of an abstract category of relations. As a result, pullback and comma toposes are calculated in a new way. The calculations are used to give a new characterization of localic morphisms and to derive interpolation and conceptual completeness properties for a certain class of interpretations between geometric theories. A simple characterization of internal sup-lattices in terms of external Sl-enriched category theory is given.

Andrew M. Pitts | A. Pitts

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