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Diagrammatic ImmanenceCategory Theory and Philosophy$
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Rocco "Gangle

Print publication date: 2015

Print ISBN-13: 9781474404174

Published to Edinburgh Scholarship Online: September 2016

DOI: 10.3366/edinburgh/9781474404174.001.0001

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Diagrams of Difference: Adjunctions and Topoi

Diagrams of Difference: Adjunctions and Topoi

Chapter:
(p.211) Chapter 6 Diagrams of Difference: Adjunctions and Topoi
Source:
Diagrammatic Immanence
Author(s):

Rocco Gangle

Publisher:
Edinburgh University Press
DOI:10.3366/edinburgh/9781474404174.003.0007

This chapter examines two advanced constructions in category theory: adjoint functors and topoi. Pairs of adjoint functors, or adjunctions, are formally defined and then illustrated with several concrete examples. Topoi are introduced conceptually by focusing on the role of the subobject classifier within a topos, with examples from set theory and graph theory. The difference between the classical logic of Boolean algebras and the non-classical logic of Heyting algebras is explained in terms of their natural mathematical environments of set theory and topos theory respectively.

Keywords:   Category theory, Adjoint functors, Adjunctions, Topoi, Non-classical logic, Heyting algebras

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