Applied Categorical Structures
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Mal’cev Conditions Revisited
Applied Categorical Structures - Tập 16 - Trang 723-733 - 2007
We characterize cosieves in locally presentable categories which are generated
by a set of objects or are even principal. We apply our results to the category
of algebraic theories where they are related to Mal’cev conditions dealt with in
universal algebra.
Pure Morphisms are Effective for Modules
Applied Categorical Structures - Tập 21 - Trang 801-809 - 2012
Yet another proof of the result asserting that a morphism of commutative rings
is an effective descent morphism for modules if and only if it is pure is given.
Moreover, it is shown that this result cannot be derived from Moerdijk’s descent
criterion.
Boundedness and Complete Distributivity
Applied Categorical Structures - Tập 9 - Trang 437-456 - 2001
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 ...
A Topological Groupoid Representing the Topos of Presheaves on a Monoid
Applied Categorical Structures - Tập 28 - Trang 749-772 - 2020
Butz and Moerdijk famously showed that every (Grothendieck) topos with enough
points is equivalent to the category of sheaves on some topological groupoid. We
give an alternative, more algebraic construction in the special case of a topos
of presheaves on an arbitrary monoid. If the monoid is embeddable in a group,
the resulting topological groupoid is the action groupoid for a discrete group
acti...
Z-Continuous Posets and Their Topological Manifestation
Applied Categorical Structures - Tập 7 - Trang 31-70 - 1999
A subset selection Z assigns to each partially ordered set P a certain
collection Z P of subsets. The theory of topological and of algebraic (i.e.
finitary) closure spaces extends to the general Z-level, by replacing finite or
directed sets, respectively, with arbitrary ‘Z-sets’. This leads to a theory of
Z-union completeness, Z-arity, Z-soberness etc. Order-theoretical notions such
as complete di...
Separation and Epimorphisms in Quasi-Uniform Spaces
Applied Categorical Structures - Tập 8 - Trang 175-207 - 2000
We study some categorical aspects of quasi-uniform spaces (mainly separation and
epimorphisms) via closure operators in the sense of Dikranjan, Giuli, and
Tholen. In order to exploit better the corresponding properties known for
topological spaces we describe the behaviour of closure operators under the
lifting along the forgetful functor T from quasi-uniform spaces to topological
spaces. By means...
Convergence Approach Spaces : Actions
Applied Categorical Structures - Tập 24 - Trang 147-161 - 2015
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
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...
A Shirota Theorem for Frames
Applied Categorical Structures - Tập 7 - Trang 271-277 - 1999
We establish a version of the Shirota Theorem which characterises
realcompactness in terms of completeness for frames; an interesting problem
considering the various notions of realcompactness for frames and the fact that
the frame completion behaves differently from its spatial counterpart. Amongst
other consequences of this characterisation, we can describe the completion of a
uniform sigma fram...
Hereditary, Additive and Divisible Classes in Epireflective Subcategories of Top
Applied Categorical Structures - Tập 16 - Trang 451-478 - 2006
Hereditary coreflective subcategories of an epireflective subcategory A of Top
such that I 2 ∉ A (here I 2 is the two-point indiscrete space) were studied in
[4]. It was shown that a coreflective subcategory B of A is hereditary (closed
under the formation subspaces) if and only if it is closed under the formation
of prime factors. The main problem studied in this paper is the question whether
thi...
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