Following earlier work, a modal logic for T -coalgebras is a functor L on a suitable variety. Syntax and proof system of the logic are given by presentations of the functor. This paper makes two contributions. First, a previous result characterizing those functors that have presentations is generalized from endofunctors on one-sorted varieties to functors between many-sorted varieties. This yie...

We discuss the use of relation lifting in the theory of set-based coalgebra and coalgebraic logic. On the one hand we prove that the neighborhood functor does not extend to a relation lifting of which the associated notion of bisimilarity coincides with behavioral equivalence. On the other hand we argue that relation liftings may be of use for many other functors that do not preserve weak pullb...

Motivated in part by the study of the stable homology of automorphism groups of free groups, we consider cohomological calculations in the category F(gr) of functors from finitely generated free groups to abelian groups. In particular, we compute the groups Ext F(gr) (T ◦a, T◦a) where a is the abelianization functor and T is the n-th tensor power functor for abelian groups. These groups are sho...

A functor is constructed from the category of globular CW-complexes to that of flows. It allows the comparison of the S-homotopy equivalences (resp. the T-homotopy equivalences) of globular complexes with the S-homotopy equivalences (resp. the T-homotopy equivalences) of flows. Moreover, it is proved that this functor induces an equivalence of categories from the localization of the category of...

A functor is constructed from the category of globular CW-complexes to that of flows. It allows to compare the S-homotopy equivalences (resp. the T-homotopy equivalences) of globular complexes with the S-homotopy equivalences (resp. the T-homotopy equivalences) of flows. Moreover, one proves that this functor induces an equivalence of categories from the localization of the category of globular...

The normalized cochain complex of a simplicial set N(Y ) is endowed with the structure of an E∞ algebra. More specifically, we prove in a previous article that N (Y ) is an algebra over the Barratt-Eccles operad (cf. [2]). According to M. Mandell, under reasonable completeness assumptions, this algebra structure determines the homotopy type of Y (cf. [14]). In this article, we construct a model...

We study the middle convolution of local systems on the punctured affine line in the singular and the étale case. We give a motivic interpretation of the middle convolution which yields information on the occurring determinants. Finally, we use these methods to realize special linear groups regularly as Galois groups over Q(t). Introduction If K is a field, then we set GK := Gal(K/K), where K d...

We consider the semigroup Ext(A, B) of extensions of a separable C *-algebra A by a stable C *-algebra B modulo unitary equivalence and modulo asymptotically split extensions. This semigroup contains the group Ext −1/2 (A, B) of invertible elements (i.e. of semi-invertible extensions). We show that the functor Ext 1/2 (A, B) is homotopy invariant and that it coincides with the functor of homoto...