Derivator
Encyclopedia
In mathematics
, derivators are a proposed new framework for homological algebra
and various generalisations. It is intended to address the perceived deficiencies of derived categories
and provide at the same time a language for homotopical algebra
.
Derivators were first introduced by Alexander Grothendieck
in his long unpublished 1983 manuscript Pursuing Stacks. They were then further developed by him in the huge unpublished 1991 manuscript Les Dérivateurs of almost 2000 pages.
The manuscript has been edited for on-line publication by Georges Maltsiniotis.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, derivators are a proposed new framework for homological algebra
Homological algebra
Homological algebra is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology and abstract algebra at the end of the 19th century, chiefly by Henri Poincaré and...
and various generalisations. It is intended to address the perceived deficiencies of derived categories
Derived category
In mathematics, the derived category D of an abelian category C is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on C...
and provide at the same time a language for homotopical algebra
Homotopical algebra
In mathematics, homotopical algebra is a collection of concepts comprising the nonabelian aspects of homological algebra as well as possibly the abelian aspects as special cases...
.
Derivators were first introduced by Alexander Grothendieck
Alexander Grothendieck
Alexander Grothendieck is a mathematician and the central figure behind the creation of the modern theory of algebraic geometry. His research program vastly extended the scope of the field, incorporating major elements of commutative algebra, homological algebra, sheaf theory, and category theory...
in his long unpublished 1983 manuscript Pursuing Stacks. They were then further developed by him in the huge unpublished 1991 manuscript Les Dérivateurs of almost 2000 pages.
The manuscript has been edited for on-line publication by Georges Maltsiniotis.