nLab Myles Tierney

Myles Tierney was a Rutgers faculty member for thirty-four years, coming to Rutgers as an Associate Professor in 1968 following positions at Rice University (1965-6) and at the ETH-Forschungsinstitut für Mathematik, Zürich (1966-68). He received his B.A. from Brown University in 1959 and his Ph.D. from Columbia in 1965.

Myles began his career as an algebraic topologist, moved toward category theory and was responsible (together with F.W. Lawvere) for the introduction of a new field within category theory: elementary topoi.

He had six Ph.D. students: Ira Wolf (1971), Carol Ann Keller (1983), Norman Adams (1984), Terence Lindgren (1984), Todd Trimble (1994), and Luca Mauri (1998). Myles retired as of January 1, 2003 and was honored by the Department at a retirement party on December 10, 2002.

(Taken from this website)

At Dalhousie he had a further Ph.D. student: Radu Diaconescu (1973).

Myles Tierney died on October 5, 2017 having turned 80 in September. He made important contributions to category theory in collaboration with Bill Lawvere and with André Joyal.

Selected writings

On monads in universal algebra and (co-)homology-theory:

• H. Applegate, M. Barr, J. Beck, F. W. Lawvere, F. E. J. Linton, E. Manes, M. Tierney, F. Ulmer: Seminar on Triples and Categorical Homology Theory, ETH 1966/67, edited by Beno Eckmann and Myles Tierney, LNM 80, Springer (1969), reprinted as: Reprints in Theory and Applications of Categories 18 (2008) 1-303 [TAC:18, pdf]

On (idemponent) monads:

• Harry Applegate, Myles Tierney, Categories with models, p. 156-244 In: Beno Eckmann (ed.) Seminar on Triples and Categorical Homology Theory Lecture Notes in Mathematics, 80, Springer 1969 [doi:10.1007/BFb0083086, pdf]

On comonads:

• Harry Applegate, Myles Tierney, Iterated cotriples, Lecture Notes in Math. 137 (1970) 56-99 (doi:10.1007/BFb0060440)

On forcing via classifying toposes and the classifying topos of a localic groupoid:

• André Joyal, Myles Tierney, An extension of the Galois theory of Grothendieck, Mem. Amer. Math. Soc. 309 (1984) [ISBN:978-1-4704-0722-3]

  (historical note: according to MR756176 (86d:18002) by Peter Johnstone, the main results of this monograph were obtained by the authors around 1978-1979, typed version circulated from 1982, and the results influenced the field much before the actual publication)

On stacks and classifying spaces:

• André Joyal and Myles Tierney, Strong stacks and classifying spaces, Category theory (Como, 1990), 213–236, Lecture Notes in Math. 1488, Springer 1991.

On the Dwyer-Kan loop groupoid-construction (path-simplicial groupoids):

• André Joyal, Myles Tierney, On the theory of path groupoids, Journal of Pure and Applied Algebra 149 1 (2000) 69-100 [doi:10.1016/S0022-4049(98)00164-9]

On the Quillen equivalence between the model categories for quasi-categories and complete Segal spaces:

• Andre Joyal, Myles Tierney, Quasi-categories vs. Segal spaces, in Categories in Algebra, Geometry and Mathematical Physics, Contemporary Mathematics 431 (2007) [arXiv:math/0607820, doi:10.1090/conm/431]

On simplicial homotopy theory, the classical model structure on simplicial sets and the classical model structure on topological spaces:

• André Joyal, Myles Tierney Notes on simplicial homotopy theory, Lecture at Advanced Course on Simplicial Methods in Higher Categories, CRM 2008 (pdf)

• André Joyal, Myles Tierney, An introduction to simplicial homotopy theory, 2009 (web, pdf)