Seminario Teoria delle Categorie.
Il giorno Giovedì 24 Marzo 2011
alle ore 11.15
presso l'aula Dottorato
del Dipartimento di Matematica
(via Saldini 50, Milano)
la dott.ssa Aurora del Rio (Università di Granada)
terrà una conferenza dal titolo:
Algebraic K-theory for categorical groups.
Abstract:
Quillen de nfied the n-th algebraic K-group of a ring R as pi_n(BGL(R)+). Using the
notion of homotopy categorical groups of any pointed space, that are de fined via the
fundamental groupoid of iterated loop spaces, in this talk, we introduce the concept of
K-categorical groups K_i(R) of any ring R. We also show the existence of a fundamental
categorical crossed module associated to any fi bre homotopy sequence. This fact, allows
us to characterize K_1(R) and K_2(R), respectively, as the homotopy cokernel and kernel of
the fundamental categorical crossed module associated to the fibre homotopy sequence
F(R) –> BGL(R) –> BGL(R)^+
Gli interessati sono cordialmente invitati.