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Applications of Sup‐Lattice Enriched Category Theory to Sheaf Theory
Author(s) -
Pitts Andrew M.
Publication year - 1988
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-57.3.433
Subject(s) - topos theory , mathematics , morphism , pure mathematics , sheaf , category theory , pullback , characterization (materials science) , class (philosophy) , category of sets , lattice (music) , subcategory , algebra over a field , functor , epistemology , art , philosophy , materials science , physics , literature , acoustics , nanotechnology
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.