Grothendieck topologies on Chu spaces

2009 ◽  
Vol 19 (3) ◽  
pp. 192-210 ◽  
Author(s):  
E. E. Skurikhin ◽  
A. G. Sukhonos
Keyword(s):  
Chu Spaces ◽  
Grothendieck Topologies

scholarly journals Coarse cohomology with twisted coefficients

2020 ◽  
Vol 70 (6) ◽  
pp. 1413-1444
Author(s):  
Elisa Hartmann
Keyword(s):  
Sheaf Cohomology ◽  
Grothendieck Topology ◽  
Coarse Structure ◽  
Relative Cohomology ◽  
Number Of Ends ◽  
Constant Coefficients ◽  
Coarse Space ◽  
Grothendieck Topologies

AbstractTo a coarse structure we associate a Grothendieck topology which is determined by coarse covers. A coarse map between coarse spaces gives rise to a morphism of Grothendieck topologies. This way we define sheaves and sheaf cohomology on coarse spaces. We obtain that sheaf cohomology is a functor on the coarse category: if two coarse maps are close they induce the same map in cohomology. There is a coarse version of a Mayer-Vietoris sequence and for every inclusion of coarse spaces there is a coarse version of relative cohomology. Cohomology with constant coefficients can be computed using the number of ends of a coarse space.

Bifinite Chu Spaces

2007 ◽  
pp. 73-74
Author(s):  
Manfred Droste ◽  
Guo-Qiang Zhang
Keyword(s):  
Chu Spaces

Grothendieck Topologies

Categories ◽  
1972 ◽  
pp. 291-319
Author(s):  
Horst Schubert
Keyword(s):  
Grothendieck Topologies

Modeling Control Flow in WS-BPEL with Chu Spaces

2011 ◽  
Vol 3 (4) ◽  
pp. 1-21 ◽  
Author(s):  
Xutao Du ◽  
Chunxiao Xing ◽  
Lizhu Zhou ◽  
Ke Han
Keyword(s):  
Process Algebra ◽  
Control Flow ◽  
Abstract Syntax ◽  
Compositional Modeling ◽  
Fault Handling ◽  
Chu Spaces

This paper presents a Chu spaces semantics of typical control flow of WS-BPEL including fault handling and link semantics. BPEL-CF is proposed as a simplification of this subset of WS-BPEL. For the compositional modeling of BPEL, the authors present a Chu spaces process algebra. This algebra allows faults to be thrown at any point of execution and take link-based synchronization into consideration. The paper gives the abstract syntax of BPEL-CF, the semantic algebra, and the valuation functions for computing the Chu spaces denotations of BPEL-CF programs.

FUZZY SETS AND FUZZY RELATIONAL STRUCTURES AS CHU SPACES

2000 ◽  
Vol 08 (04) ◽  
pp. 471-479 ◽  
Author(s):  
BASIL K. PAPADOPOULOS ◽  
APOSTOLOS SYROPOULOS
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Linear Logic ◽  
Relational Structure ◽  
Mathematical Structures ◽  
Relational Structures ◽  
Chu Spaces

Chu spaces, which derive from the Chu construct of *-autonomous categories, can be used to represent most mathematical structures. Moreover, the logic of Chu spaces is linear logic. Most efforts to incorporate fuzzy set theory into the realm of linear logic are based on the assumption that fuzzy and linear negation are identical operations. We propose an incorporation based on the opposite assumption and we provide an interpretation of some linear connectives. Furthermore, we show that it is possible to represent any fuzzy relational structure as a Chu space by means of the functor G.

scholarly journals Lattice-Valued Topological Systems as a Framework for Lattice-Valued Formal Concept Analysis

2013 ◽  
Vol 2013 ◽  
pp. 1-33 ◽  
Author(s):  
Sergey A. Solovyov
Keyword(s):  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Formal Concept ◽  
Galois Connections ◽  
Chu Spaces

Recently, Denniston, Melton, and Rodabaugh presented a new categorical outlook on a certain lattice-valued extension of Formal Concept Analysis (FCA) of Ganter and Wille; their outlook was based on the notion of lattice-valued interchange system and a category of Galois connections. This paper extends the approach of Denniston et al. clarifying the relationships between Chu spaces of Pratt, many-valued formal contexts of FCA, lattice-valued interchange systems, and Galois connections.

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