(Co)homology of crossed modules with coefficients in a π1\pi_1-module

We define a cotriple (co)homology of crossed modules with coefficients in a $\pi_1$-module. We prove its general properties, including the connection with the existing cotriple theories on crossed modules. We establish the relationship with the (co)homology of the classifying space of a crossed module and with the cohomology of groups with operators. An example and an application are given.Comment: 32 pages, LaTeX2e, Paul Taylor's diagram package; added reference. Accepted for publication by Homology, Homotopy and Application

The Weakly Globular Double Category of Fractions of a Category

This paper introduces the construction of a weakly globular double category of fractions for a category and studies its universal properties. It shows that this double category is locally small and considers a couple of concrete examples.Comment: 73 pages. arXiv admin note: substantial text overlap with arXiv:1210.405