# Joyal's CatLab Gabriel, Pierre

Pierre Gabriel is a Swiss mathematician. He studied under the direction of Grothendieck and received his Phd from the University of Paris in 1961 with a thesis on abelian categories. A version of his thesis was published as Des catégories abéliennes. Students of Gabriel include Bernhard Keller.

In his book with Michel Zisman?, Calculus of Fractions and Homotopy Theory, Gabriel introduced a general localization method in homotopy theory (see also calculus of fractions?). Many ideas introduced in the book were developed further by Daniel Quillen in his Homotopical Algebra?.

Gabriel has also an important contribution to pure category theory with Friedrich Ulmer? on locally presentable categories?:

• P. Gabriel, F. Ulmer, Lokal präsentierbare Kategorien

In later part of his mathematical career, Gabriel worked on representation theory of finite-dimensional associative algebras and quivers, where he found some of the basic theorems.

For other information, see the $n$Lab page Pierre Gabriel.

category: people
Revised on May 9, 2013 at 23:00:05 by Tim Porter