Cohomology of the Grothendieck construction

PIRASHVILI, TEIMURAZ; REDONDO, MARIA JULIA

Colonia del Sacramento

Congreso; XVI Coloquio Latinoamericano de Algebra; 2005

Universidad de la República, Montevideo

Given a small category K and a functor L : K -> CAT, there is a well defined category S(L) called the Grothendieck construction of L.  We consider the cohomology of the Grothendieck construction of L with coefficients in a natural system D, in the sense of Baues and Wirsching. We show that there exists a spectral sequence abutting to the cohomology of the Grothendieck construction of L in terms of the cohomology of K and of L(k), for k an object in K.