nLab Philip Higgins

Philip J. Higgins (1926-2015) was a British mathematician, who worked in areas of algebra and algebraic topology. He is author of a book on categories and groupoids [Higgins 1971]. In later years Higgins worked with Ronnie Brown.

Selected writings

On categories and groupoids:

• Philip J. Higgins, Categories and Groupoids, Mathematical Studies 32, van Nostrand New York (1971), Reprints in Theory and Applications of Categories 7 (2005) 1-195 [tac:tr7, pdf]

On algebraic topology using strict ∞-groupoids (often in the equivalent guise of crossed complexes, slightly “nonabelian” chain complexes):

• Ronnie Brown, Philip Higgins, Rafael Sivera: Nonabelian Algebraic Topology: filtered spaces, crossed complexes, cubical homotopy groupoids, Tracts in Mathematics 15, European Mathematical Society (2011) [ISBN 978-3-03719-083-8, doi:10.4171/083, webpage]

For more on his long standing collaboration with Ronnie Brown on nonabelian algebraic topology, see here.

His earlier paper

• P. J. Higgins, Algebras with a scheme of operators, Math. Nachr. 27 (1963) 115–132.

has been influential: it deals with partial operations, following on from his paper

• P. J. Higgins, Groups with multiple operators, Proc London Math. Soc. VI (1956) 366-416.

His paper

• P. J. Higgins, The fundamental groupoid of a graph of groups, J. London Math. Soc. (2), 13 (1976) 145–149,

developed methods that were later on used by Haefliger in assigning a groupoid to a complex of groups.

More recently he had worked with Kirill Mackenzie on Lie groupoids and Lie algebroids

category: people