We show that for any set of disjoint line segments in the plane there exists a pointed binary encompassing tree T , that is, a spanning tree on the segment endpoints that contains all input segments, has maximum degree three, and every vertex v ∈ T is pointed, that is, v has an incident angle greater than π. Such a tree can be completed to a minimum pseudo-triangulation. In particular, it follo...

This paper proves that the functor C(∗) that sends pointed, simply-connected CW-complexes to their chain-complexes equipped with diagonals and iterated higher diagonals, determines their integral homotopy type — even inducing an equivalence of categories between the category of CW-complexes up to homotopy equivalence and a certain category of chain-complexes equipped with higher diagonals. Cons...

Empirical attempts to understand connections between abstract cognition and sensori-motor processes have pointed toward an embodied view of cognition, where cognitive activity is strongly tied to sensori-motor activity. Here the authors test the ability of the cognitive system to impose structure on the world using a well-established phenomenon in spatial cognition--biases near spatial category...

We develop some techniques to the study of exact module categories over some families of pointed finite-dimensional Hopf algebras. As an application we classify exact module categories over the tensor category of representations of the small quantum groups uq(sl2).

Existence of superdecomposable pure-injective modules reflects complexity in the category of finite-dimensional representations. We describe the relation in terms of pointed modules. We present methods for producing superdecomposable pure-injectives and give some details of recent work of Harland doing this in the context of tubular algebras. 2010 Mathematics Subject Classification. Primary 16G...

Working in an arbitrary pointed proper model category, we describe the cofibrations that have an obstruction theory with respect to all fibrations. Up to weak equivalence, retract, and cobase change, they are the cofibrations with weakly contractible target. Equivalently, they are the retracts of principal cofibrations. Without properness, the same classification holds for cofibrations with cof...

We extend the W-construction of Boardman and Vogt to operads of an arbitrary monoidal model category with suitable interval, and show that it provides a cofibrant resolution for well-pointed Σ-cofibrant operads. The standard simplicial resolution of Godement as well as the cobar-bar chain resolution are shown to be particular instances of this generalised W-construction.

As is pointed out in [Smith (1997)], in many applications of quasigroups isotopies and homotopies are more important than isomorphisms and homomorphisms. In this paper, the way homotopies may arise in the context of categorical quasigroup model theory is investigated. In this context, the algebraic structures are specified by diagram-based logics, such as sketches, and categories of models beco...

Quite a number of models have been proposed under the name of structured analysis and design. It has been pointed out, however, that there is no common theoretical framework among them. Transformation of a specification from one model to another, although often recommended by authors, can only be done manually. A category-theoretic approach is proposed in this paper. As a result, development of...

In this work, using the functoriality of Drinfeld center fusion categories, we generalize full simple separable algebras in a fixed category to all categories. This generalization produces new functor, which involves both and is called pointed functor. We prove that functor symmetric monoidal equivalence. It turns out provides precise rather complete mathematical formulation boundary-bulk relat...