Skip to main content

On universal algebra over nominal sets


We investigate universal algebra over the category Nom of nominal sets. Using the fact that Nom is a full reflective subcategory of a monadic category, we obtain an HSP-like theorem for algebras over nominal sets. We isolate a ‘uniform’ fragment of our equational logic, which corresponds to the nominal logics present in the literature. We give semantically invariant translations of theories for nominal algebra and NEL into ‘uniform’ theories, and systematically prove HSP theorems for models of these theories.

Hide All
Adámek, J., Herrlich, H. and Strecker, G. E. (1990) Abstract and Concrete Categories, John Wiley and Sons.
Adámek, J. and Rosický, J. (1994) Locally Presentable and Accessible Categories, Cambridge University Press.
Adámek, J., Rosický, J. and Vitale, E. M. (draft) Algebraic Theories: a Categorical Introduction to General Algebra. Available at
Bonsangue, M. and Kurz, A. (2007) Pi-calculus in logical form. 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007) 303–312.
Bonsangue, M. M. and Kurz, A. (2006) Presenting functors by operations and equations. In: FoSSaCS. Springer-Verlag Lecture Notes in Computer Science 3921.
Borceux, F. (1994) Handbook of Categorical Algebra, Cambridge University Press.
Clouston, R. and Pitts, A. (2007) Nominal equational logic. In: Computation, Meaning and Logic: Articles dedicated to Gordon Plotkin. Electronic Notes in Theoretical Computer Science 172.
Fiore, M., Plotkin, G. and Turi, D. (1999) Abstract syntax and variable binding. Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science 193–202.
Fiore, M. P. and Hur, C.-K. (2008) Term equational systems and logics (extended abstract). Electronic Notes in Theoretical Computer Science 218 171192.
Gabbay, M. (2008) Nominal algebra and the HSP theorem. Journal of Logic and Computation 19 (2)341367.
Gabbay, M. and Pitts, A. (1999) A new approach to abstract syntax involving binders. Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science (LICS'99) 214–224.
Gabbay, M. J. and Mathijssen, A. (2009) Nominal (universal) algebra: equational logic with names and binding. Journal of Logic and Computation (in press).
Johnstone, P. T. (2002) Sketches of an Elephant: A Topos Theory Compendium, vol. 1, Oxford Logic Guides 43, Oxford University Press.
Kurz, A. and Petrişan, D. (2008) Functorial coalgebraic logic: The case of many-sorted varieties. In: Adámek, J. and Kupke, C. (eds.) Proceedings of the Ninth Workshop on Coalgebraic Methods in Computer Science (CMCS 2008). Electronic Notes in Theoretical Computer Science 203 (5)175194
Kurz, A. and Rosický, J. (2006) Strongly complete logics for coalgebras (submitted).
Mac Lane, S. and Moerdijk, I. (1994) Sheaves in Geometry and Logic: A First Introduction to Topos Theory (Universitext), Springer-Verlag.
Stark, I. (2008) Free-algebra models for the pi -calculus. Theoretical Computer Science 390 (2-3)248270.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 19 *
Loading metrics...

Abstract views

Total abstract views: 91 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 22nd March 2018. This data will be updated every 24 hours.