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A Higher-Order Calculus for Categories

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Book cover Theorem Proving in Higher Order Logics (TPHOLs 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2152))

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Abstract

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.

PhD student at BRICS, Centre of the Danish National Research Foundation.

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Author information

Authors and Affiliations

  1. Computer Laboratory, University of Cambridge, Cambridge

    Mario Cáccamo & Glynn Winskel

Authors
  1. Mario Cáccamo
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  2. Glynn Winskel
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Editor information

Editors and Affiliations

  1. Department of Computing Science, University of Glasgow, 17 Lilybank Gardens, Glasgow, G12 8QQ, Scotland, UK

    Richard J. Boulton

  2. Division of Informatics, University of Edinburgh, James Clerk Maxwell Building, King’s Buildings, Edinburgh, EH9 3JZ, Scotland, UK

    Paul B. Jackson

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© 2001 Springer-Verlag Berlin Heidelberg

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Cáccamo, M., Winskel, G. (2001). A Higher-Order Calculus for Categories. In: Boulton, R.J., Jackson, P.B. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2001. Lecture Notes in Computer Science, vol 2152. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44755-5_11

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  • DOI: https://doi.org/10.1007/3-540-44755-5_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42525-0

  • Online ISBN: 978-3-540-44755-9

  • eBook Packages: Springer Book Archive

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