We recall Hoare's formulation of data re nement in terms of upward, downward and total simulations between locally ordered functors from the structured locally ordered category generated by a programming language with an abstract data type to a semantic locally ordered category: we use a simple imperative language with a data type for stacks as leading example. We give a uni ed category theoret...

In this article, we study feedback linearization problems for nonlinear differential-algebraic control systems (DACSs). We consider two kinds of equivalences, namely, external equivalence, which is defined (locally) on the whole generalized state space, and internal locally maximal controlled invariant submanifold (i.e., set where solutions exist). define a notion called explicitation with driv...

In this paper we continue our algebraic approach to the study of locally analytic representations of a p-adic Lie group G in vector spaces over a non-Archimedean complete field K. We characterize the smooth representations of Langlands theory which are contained in the new category. More generally, we completely determine the structure of the representations on which the universal enveloping al...

In the context of semi-abelian categories, several additional conditions have been considered in order to obtain a closer group-like behavior. Among them are locally algebraic cartesian closedness and algebraic coherence. The recent notion of S-protomodular categories, whose main examples are the category of monoids and, more generally, categories of monoids with operations and Jónsson-Tarski v...

The Milnor-Hirzebruch class of a locally complete intersection X in an algebraic manifold M measures the difference between the (Poincaré dual of the) Hirzebruch class of the virtual tangent bundle of X and, respectively, the Brasselet-Schürmann-Yokura (homology) Hirzebruch class of X . In this note, we calculate the Milnor-Hirzebruch class of a globally defined algebraic hypersurface X in term...

We characterize those Lie groups (as well as algebraic groups over a local field of characteristic zero) whose first reduced L-cohomology is zero for all p > 1, extending a result of Pansu. As an application, we obtain a description of Gromov-hyperbolic groups among those groups. In particular we prove that any non-elementary Gromov-hyperbolic algebraic group over a non-Archimedean local field ...

1.1. Principal G-bundles. Topology is concerned with topological spaces and continuous maps between them. But the data is a topological space of so complicated and infinite in nature that it can be very difficult even to tell when two topological spaces are “the same.” For instance, all n-dimensional manifolds look locally the same. A central theme in algebraic topology is to attach algebraic i...

The Milnor-Hirzebruch class of a locally complete intersection X in an algebraic manifold M measures the difference between the (Poincaré dual of the) Hirzebruch class of the virtual tangent bundle of X and, respectively, the Brasselet-Schürmann-Yokura (homology) Hirzebruch class of X. In this note, we calculate the Milnor-Hirzebruch class of a globally defined algebraic hypersurface X in terms...

Lawvere theories provide a categorical formulation of the algebraic theories from universal algebra. Freyd categories are categorical models of first-order effectful programming languages. The notion of sound limit doctrine has been used to classify accessible categories. We provide a definition of Lawvere theory that is enriched in a closed category that is locally presentable with respect to ...

In this paper various properties of the spectrum (i.e. the set of prime elements endowed with the hull-kernel topology) of a distributive continuous lattice are developed. It is shown that the spectrum is always a locally quasicompact sober space and conversely that the lattice of open sets of a locally quasicompact sober space is a continuous lattice. Algebraic lattices are a special subclass ...