Diagrams of Difference: Adjunctions and Topoi
Diagrams of Difference: Adjunctions and Topoi
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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