Applied Categorical Structures

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Boundedness and Complete Distributivity
Applied Categorical Structures - Tập 9 - Trang 437-456 - 2001
R. Rosebrugh, R. J. Wood
We extend the concept of constructive complete distributivity so as to make it applicable to ordered sets admitting merely bounded suprema. The KZ-doctrine for bounded suprema is of some independent interest and a few results about it are given. The 2-category of ordered sets admitting bounded suprema over which inhabited (classically non-empty) infima distribute is shown to be bi-equivalent to a ...... hiện toàn bộ
Convergence Approach Spaces : Actions
Applied Categorical Structures - Tập 24 - Trang 147-161 - 2015
E. Colebunders, H. Boustique, P. Mikusiński, G. Richardson
Properties of continuous actions and pseudoquotients are studied in the category of convergence approach spaces. Invariance properties of continuous actions on convergence approach spaces are given. It is shown that the formation of pseudoquotient spaces is idempotent. Function space actions are also investigated.
Maximal Classes of Topological Spaces and Domains Determined by Function Spaces
Applied Categorical Structures - Tập 11 - Trang 391-402 - 2003
Jimmie D. Lawson, Luoshan Xu
In this paper the question of what classes A of T 0-spaces should be paired with classes ℬ of domains in order that all function spaces [A→B] for A∈A and B∈ℬ are λ-compact domains is considered. It is shown that core compact spaces are paired with bounded complete domains and a class of topological spaces called RW-spaces (with finitely many components) is paired with the class of λ-compact pointe...... hiện toàn bộ
Adjunctions and Locally Transferable Factorization Systems
Applied Categorical Structures - Tập 9 - Trang 625-650 - 2001
D. Zangurashvili
We present an approach to construct factorization systems in abstract categories. It gives new factorization systems from some given ones, when we have a relevant family of adjunctions between slice categories. The approach is based on the notion of a local factorization system, which is introduced in this paper. Relations between local factorization systems and full replete reflective subcategori...... hiện toàn bộ
Merotopological Spaces
Applied Categorical Structures - Tập 12 - Trang 155-180 - 2004
H. L. Bentley, H. Herrlich
In this paper we introduce a new topological-type of structured set called merotopological space. The appropriate morphisms are defined and characterizations of the corresponding initial and final structures are given. The resulting category contains as fully embedded subcategories not only the category of topological spaces and continuous maps but also the category of merotopic spaces and uniform...... hiện toàn bộ
A Characterization of n-Gorenstein Tilting Comodules
Applied Categorical Structures - Tập 30 - Trang 1135-1152 - 2022
Yexuan Li, Hailou Yao
The aim of this paper is to introduce the concept of n-Gorenstein tilting comodules and study its main properties. This concept generalizes the notion of n-tilting comodules of finite injective dimensions to the case of finite Gorenstein injective dimensions. As an application of our results, we discuss the problem of existence of complements to partial n-Gorenstein tilting comodules.
Iterated Chromatic Subdivisions are Collapsible
Applied Categorical Structures - Tập 23 - Trang 777-818 - 2014
Éric Goubault, Samuel Mimram, Christine Tasson
The standard chromatic subdivision of the standard simplex is a combinatorial algebraic construction, which was introduced in theoretical distributed computing, motivated by the study of the view complex of layered immediate snapshot protocols. A most important property of this construction is the fact that the iterated subdivision of the standard simplex is contractible, implying impossibility re...... hiện toàn bộ
Non-Pointed Strongly Protomodular Theories
Applied Categorical Structures - Tập 12 Số 4 - Trang 319-338 - 2004
Borceux, F.
We give criterions for strong protomodularity and prove that the strong protomodularity of an algebraic theory is inherited by its models in a category with finite limits. We give examples of strongly protomodular theories with several constants: C *-algebras, rings, Heyting algebras and Boolean algebras.
Non-symmetric Exponential Laws in the Construct PRTOP
Applied Categorical Structures - Tập 10 - Trang 251-256 - 2002
M. Sioen
We show that the construct PRTOP of pre-topological spaces and continuous maps admits a proper class of monoidal closed structures.
Structured Frames by Weil Entourages
Applied Categorical Structures - Tập 8 - Trang 351-366 - 2000
Jorge Picado
In the framework of pointfree topology, we discuss the rôle of Weil entourages in the study of structures such as uniformities, quasi-uniformities, nearnesses, quasi-nearnesses, proximities and infinitesimal relations.
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