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FUNCTORS AND NATURALITY

Steve Awodey

in Category Theory

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198568612
eISBN:
9780191717567
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568612.003.0007
Subject:
Mathematics, Algebra

This chapter develops a general theory for functors. Topics discussed include category of categories, representable structure, stone duality, naturality, examples of natural transformations, ... More


Categories and Modalities

Kohei Kishida

in Categories for the Working Philosopher

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198748991
eISBN:
9780191811593
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198748991.003.0009
Subject:
Philosophy, History of Philosophy

Category theory provides various guiding principles for modal logic and its semantic modeling. In particular, Stone duality, or “syntax-semantics duality”, has been a prominent theme in semantics of ... More


Types and Stone spaces

Tim Button and Sean Walsh

in Philosophy and Model Theory

Published in print:
2018
Published Online:
May 2018
ISBN:
9780198790396
eISBN:
9780191863424
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198790396.003.0014
Subject:
Philosophy, Logic/Philosophy of Mathematics

Types are one of the cornerstones of contemporary model theory. Simply put, a type is the collection of formulas satisfied by an element of some elementary extension. The types can be organised in an ... More


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