In this paper we study topology of moduli spaces of tropical curves of genus g with n marked points. We view the moduli spaces as being imbedded in a larger space, which we call the moduli space of metric graphs with n marked points. We describe the shrinking bridges strong deformation retraction, which leads to a substantial simplification of all these moduli spaces. In the rest of the paper, ...

An introduction to the notions of homotopy limit and colimit is given. It is explained how they can be used to neatly describe the “old” distinguished triangles and shift functors of derived categories resp. cofiber and fiber sequences in algebraic topology. One of the goals is to motivate the language of derivators from the perspective of classical homological algebra. Another one is to give e...

Extended Abstract The concept of reenement is a well-known technique within software engineering in general and for stepwise development of Petri nets in particular. In fact, several diierent concepts for the reenement of nets have been proposed in literature, above all the reenement of places, transitions or even subnets by some other subnet. Based on the idea of formal grammars, we propose ru...

For the free topological group on an interval [a, b] a family of closed, locally path-connected subgroups is given such that each group is not projective and so not free topological. Simplicial methods are used, and the test for nonprojectivity is nonfreeness of the group of path components. Similar results are given for the abelian case. Introduction. Let F(X) be the free topological group on ...

Double categories were introduced by Ehresmann [Ehr65] as an example of structured category. Examples of double groupoids were shown to arise from crossed modules in [BS76b, BS76a] and this result was applied in [BH78] to give a 2-dimensional version of the Van Kampen Theorem for the fundamental group, namely a colimit theorem for the fundamental crossed module of a based pair. These results we...

Objects are presented as processes endowed with state-dependent slots. Active objects have non-quiescent states. A morphism between two objects expresses that the source object is part-of the target object, in such a way that the possible observations of the part, considered in isolation, are constrained within the whole. Our semantic domain for object-oriented concepts includes a cocomplete ca...

To every affine real arrangement of hyperplanes AR we associate a family of diagrams of spaces over the face poset of the arrangement. We show that any cover of the complement of the complexification of AR is homotopy equivalent to the homotopy colimit of one of the diagrams. More precisely, we show that any cover of the Salvetti complex is isomorphic to the order complex of the poset limit of ...

Our work over the past years shows that not only the collection of (for instance) all topological spaces gives rise to a category, but also each topological space can be seen individually as a category by interpreting the convergence relation x −→ x between ultrafilters and points of a topological space X as arrows in X. Naturally, this point of view opens the door to the use of concepts and id...

Although there is now some agreement with the view that the supply of photochemical energy may influence photosynthetic rate (P) at high CO2 pressures, it is less clear whether this limitation extends to P at low CO2. This was investigated by measuring P per area as a function of the intercellular CO2 concentration (C,) at different levels of photochemical energy supply. Changes in the latter w...

Conceptual blending has been employed very successfully to understand the process of concept invention, studied particularly within cognitive psychology and linguistics. However, despite this influential research, within computational creativity little effort has been devoted to fully formalise these ideas and to make them amenable to computational techniques. We here present the basic formalis...