On the Notion of PrecohomologyPortugaliae Mathematica
AbstractABSTRACT. For a cochain complex one can have the cohomology functor. In this paper we introduce the notion of precohomology for a cochain that is not a complex, i. e., dq+1 o dq may not be zero. Such a cochain, with objects and morphisms of an abelian category A, is called a cochain precomplex whose category is denoted by Pco (A). If a cochain precomplex is actually a cochain complex, then the notion of precohomology coincides with that of cohomology, i. e., precohomology is a gene¬ralization of cohomology. For a left exact functor F from an abelian category A to an abelian category B, the hyperprecohomology of F is defined, and some properties are given. In the last section, a generalization of an inverse limit, called a prein¬verse limit, is introduced. We discuss some of the links between precohomology and preinverse limit.
Copyright1985 European Mathematical Society (EMS).
Citation InformationGoro Kato. "On the Notion of Precohomology" Portugaliae Mathematica Vol. 43 Iss. 3 (1985) p. 307 - 316
Available at: http://works.bepress.com/gkato/5/