Modern Logic — A Survey pp 235-252 | Cite as

# Logic and Category Theory

## Abstract

In spite of the title, this paper deals with one aspect only of the interconnections between logic and category theory, namely the dialectics of ‘concept’ versus ‘Variable set’ or, more precisely, the connections between model theory and topos theory. The connections between proof theory and category theory have been completely left out and the interested reader is referred to [22], where a full account of the work done in that area may be found. Furthermore, since a survey article on the connections between model theory and topos theory has recently appeared [10], I shall rather concentrate on one particular problem: to formulate rigourously the ‘principle’ that ‘in the infinitely small, every function is linear’ (Although this ‘principle’ was one of the fundamental intuitions that helped to develop calculus in the 17th Century, it did not survive the ‘Arithmetization of Analysis’ in the 19th and was swept out as hopelessly wrong along with infinitesimals, fluxions, etc.).

## Keywords

Topological Space Category Theory Intuitionistic Logic Adjointness Condition Intended Interpretation## Preview

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