Categorical Logic

Categorical logic is a branch of category theory within mathematics, adjacent to mathematical logic but more notable for its connections to theoretical computer science. In broad terms, categorical logic represents both syntax and semantics by a category, and an interpretation by a functor. The categorical framework provides a rich conceptual background for logical and type-theoretic constructions. The subject has been recognisable in these terms since around 1970.

Read more about Categorical LogicOverview, Historical Perspective

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Categorical Logic - Historical Perspective
... Categorical logic originated with William Lawvere's Functorial Semantics of Algebraic Theories (1963), and Elementary Theory of the Category of Sets (1964) ... thus establishing the fruitful field of topos theory, which provides a unified categorical treatment of the syntax and semantics of higher-order predicate logic ... The resulting logic is formally intuitionistic ...

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