nLab Martin Hyland

John Martin Elliott Hyland is Professor in Mathematical Logic in the University of Cambridge, and is a Fellow of King’s College, Cambridge. Hyland is known for work on the effective topos (within topos theory), on the lambda-calculus and on game semantics.

His main research interests are in the following.

• Mathematical Logic: Lambda Calculus, Recursion Theory, Realizability, Proof Theory, Linear Logic.

• Category Theory: Topos Theory, Categorical algebra, Operads, Higher-dimensional Categories.

• Theoretical Computer Science: Applications of Category Theory, Domain Theory, Polymorphism, Game Semantics.

Links:

• personal webpage

• institute webpage

• research page

• Wikipedia entry

Selected writings

On categorical semantics for the exponential modality in linear logic:

• Nick Benton, Gavin Bierman, Valeria de Paiva, Martin Hyland, Linear $\lambda$-Calculus and Categorical Models Revisited, in Computer Science Logic. CSL 1992, Lecture Notes in Computer Science 702, Springer (1993) [doi:10.1007/3-540-56992-8_6]

On realizability and the propositional axiom of choice:

• Martin Hyland, Variations on realizability: realizing the propositional axiom of choice, Mathematical Structures in Computer Science, Volume 12 , Issue 3 , June 2002 , pp. 295 - 317 (doi:10.1017/S0960129502003651, pdf)

On categorical semantics for linear logic:

• Martin Hyland, Andrea Schalk, Glueing and orthogonality for models of linear logic, Theoretical Computer Science 294 1–2 (2003) 183-231 [doi:10.1016/S0304-3975(01)00241-9]

On the history of categorical universal algebra via Lawvere theories and monads:

• Martin Hyland, John Power, The Category Theoretic Understanding of Universal Algebra: Lawvere Theories and Monads, Electronic Notes in Theor. Comp. Sci. 172 (2007) 437-458 [doi:10.1016/j.entcs.2007.02.019, preprint]

category: people