Priestley-type dualities for partially ordered structures

Caramello, Olivia

doi:10.1016/j.apal.2016.04.008

Cited by 1 publication

(2 citation statements)

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“…. This result was used in [10] and [13] to build spectra for various kinds of partially ordered structures and, combined with other results, Stone-type and Priestley-type dualities for them.…”

Section: Geometric Morphismsmentioning

confidence: 99%

“…• Categorical dualities or equivalences between 'concrete' categories can often be seen as arising from the process of 'functorializing' Morita-equivalences which express structural relationships between each pair of objects corresponding to each other under the given duality or equivalence (cf. for example [10], [13] and [14]). In fact, the theory of geometric morphisms of toposes provides various natural ways of 'functorializing' bunches of Morita-equivalences.…”

Section: Decks Of 'Bridges': Morita-equivalencesmentioning

confidence: 99%

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Topos-theoretic background

Caramello¹

2018

Oxford Scholarship Online

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This chapter provides the topos-theoretic background necessary for understanding the contents of the book; the presentation is self-contained and only assumes a basic familiarity with the language of category theory. The chapter begins by reviewing the basic theory of Grothendieck toposes, including the fundamental equivalence between geometric morphisms and flat functors. Then it presents the notion of first-order theory and the various deductive systems for fragments of first-order logic that will be considered in the course of the book, notably including that of geometric logic. Further, it discusses categorical semantics, i.e. the interpretation of first-order theories in categories possessing ‘enough’ structure. Lastly, the key concept of syntactic category of a first-order theory is reviewed; this notion will be used in Chapter 2 for constructing classifying toposes of geometric theories.

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Section: Geometric Morphismsmentioning

confidence: 99%

Section: Decks Of 'Bridges': Morita-equivalencesmentioning

confidence: 99%