We introduce posets with interfaces (iposets) and generalise their standard serial composition to a new gluing composition. In the partial order semantics of concurrency, allow modelling events that extend in time across components. Alternatively, taking decompositional view, cutting through events, while may only cut edges poset. show iposets under form category, which generalises monoid up is...

In this paper we revisit some pioneering efforts to equip Petri nets with compact operational models for expressing causality. The models we propose have a bisimilarity relation and a minimal representative for each equivalence class, and they can be fully explained as coalgebras on a presheaf category on an index category of partial orders. First, we provide a set-theoretic model in the form o...

We prove that the bounded derived category of coherent sheaves on a smooth projective complex variety reconstructs isomorphism classes fibrations onto curves genus g?2. Moreover, in dimension at most four, we same normal surfaces with positive holomorphic Euler characteristic and admitting finite morphism to an abelian variety. Finally, study invariance class minimal base under condition all Ho...

We construct the stable (representable) homotopy category of finite orbispectra, whose objects are formal desuspensions orbi-CW-pairs by vector bundles and morphisms classes relative maps. The representable orbispectra admits a contravariant involution extending Spanier--Whitehead duality. This duality relates homotopical cobordism theories (cohomology on orbispectra) represented global Thom sp...

Let G be a connected reductive complex algebraic group, and E elliptic curve. GE denote the component of trivial bundle in stack semistable G-bundles on E. We introduce analytic uniformization by adjoint quotients subgroups loop group G. This can viewed as nonabelian version classical E≃C⁎/qZ. similarly construct itself via exponential map, providing standard isomorphism C⁎≃C/Z, generalizing pr...

Main contribution of this paper is an investigation of expressive power of the database category DB. An object in this category is a database-instance (set of n-ary relations). Morphisms are not functions but have complex tree structures based on a set of complex query computations. They express the semantics of view-based mappings between databases. The higher (logical) level scheme mappings b...

A notion of simulation of one datatype by another is deened as a constructive preorder. A calculus of datatype simulation is then developed by formulating constructive versions of least-xed-point theorems in lattice theory. The calculus is applied to the construction of several isomorphisms between classes of datatypes. In particular constructive adaptations of theorems in lattice theory about ...

For a long period the theory of modules over rings on the one hand and comodules and Hopf modules for coalgebras and bialgebras on the other side developed quite independently. In this talk we want to outline how ideas from module theory can be applied to enrich the theory of comodules and vice versa. For this we consider A-corings C with grouplike elements over a ring A, in particular Galois c...

Let Cat be the category whose objects are small categories (categories whose collection of objects are sets) and whose morphisms Cat(C,D) from category C to category D are functors F : C → D. Let Set be the category whose objects are sets and given x, y ∈ Ob(Set) morphisms in Set from x to y are maps f : x → y. We define an equivalence relation IsoC on Ob(C) as follows: two objects x and y are ...

We propose to prove a theorem analogues to the duality theorem on the étale cohomology of schemes proved by Grothendieck ([SGA72a, SGA72b, SGA73] and [Ver67]). This theorem generalize the classical theorem of Poincaré duality on topological spaces and more generally homological and cohomological varieties ([Bor57] and [BM60]). We will utilize hypercohomology as well as derived categories of abe...