A Higher-Order Calculus for Categories

Mario Jose Cáccamo, Glynn Winskel


A calculus for a fragment of category theory is presented. The types in the language denote categories and the expressions functors. The judgements of the calculus systematise categorical arguments such as: an expression is functorial in its free variables; two expressions are naturally isomorphic in their free variables. There are special binders for limits and more general ends. The rules for limits and ends support an algebraic manipulation of universal constructions as opposed to a more traditional diagrammatic approach. Duality within the calculus and applications in proving continuity are discussed with examples. The calculus gives a basis for mechanising a theory of categories in a generic theorem prover like Isabelle.

Full Text:


DOI: http://dx.doi.org/10.7146/brics.v8i27.21687
This website uses cookies to allow us to see how the site is used. The cookies cannot identify you or any content at your own computer.

ISSN: 0909-0878 

Hosted by the Royal Danish Library and Aarhus University Library