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Abstract: This dissertation studies the logic underlying category theory. In particular we present a formal calculus for reasoning about universal properties. The aim is to systematise judgements about functoriality and naturality central to categorical reasoning. The calculus is based on a language which extends the typed lambda calculus with new binders to represent universal constructions. The types of the languages are interpreted as locally small categories and the expressions represent functors.... (Update)
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BibTeX entry: (Update)
@misc{ caccamo-formal,
author = "Mario José Caccamo",
title = "A Formal Calculus for Categories",
url = "citeseer.ist.psu.edu/caccamo03formal.html" }
Citations (may not include all citations):382 Lambda calculi with types - Barendregt - 1992
359 Introduction to Higher Order Categorical Logic (context) - Lambek, Scott - 1986
233 The formulae-as-types notion of construction (context) - Howard - 1990
232 Category Theory for Computing Science (context) - Barr, Wells - 1990
229 Foundations of Programming Languages (context) - Mitchell - 1996
129 The foundation of a generic theorem prover - Paulson - 1988
99 volume 5 of Graduate Texts in Mathematics (context) - Lane, the et al. - 1998
69 Information and Computation (context) - Joyal, Nielsen et al. - 1996
69 Abstract syntax and variable binding (context) - Fiore, Plotkin et al. - 1999
67 Towards a mathematical operational semantics - Turi, Plotkin - 1997
66 What is a categorical model of intuitionistic linear logic - Bierman - 1995
65 Sheaves in Geometry and Logic: A First Introduction to Topos.. (context) - Lane, Moerdijk - 1992
63 Theoretical Computer Science (context) - Bainbridge, Freyd et al. - 1990
63 Theoretical Computer Science (context) - Freyd - 2002
60 A term calculus for intuitionistic linear logic - Benton, Bierman et al. - 1993
[Article contains additional citations not shown here]
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