2021-07-26T05:46:49Z
https://cgasa.sbu.ac.ir/?_action=export&rf=summon&issue=1600
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2015
3
1
Cover
2015
07
01
https://cgasa.sbu.ac.ir/article_10826_d6b982e28d79da71c67a42d774514343.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2015
3
1
Subpullbacks and coproducts of $S$-posets
Xingliang
Liang
Yanfeng
Luo
In 2001, S. Bulman-Fleming et al. initiated the study of three flatness properties (weakly kernel flat, principally weakly kernel flat, translation kernel flat) of right acts $A_{S}$ over a monoid $S$ that can be described by means of when the functor $A_{S} \otimes -$ preserves pullbacks. In this paper, we extend these results to $S$-posets and present equivalent descriptions of weakly kernel po-flat, principally weakly kernel po-flat and translation kernel po-flat. Moreover, we show that most of flatness properties of $S$-posets can be transferred to their coproducts and vice versa.
$S$-poset
subpullback
flatness
coproduct
2015
07
01
1
20
https://cgasa.sbu.ac.ir/article_8992_c4f4ba1f7b36eaeed79d6c77c92e6f45.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2015
3
1
Actions of a separately strict cpo-monoid on pointed directed complete posets
Halimeh
Moghbeli Damaneh
In the present article, we study some categorical properties of the category {$\bf Cpo_{Sep}$-$S$} of all {separately strict $S$-cpo's}; cpo's equipped with a compatible right action of a separately strict cpo-monoid $S$ which is strict continuous in each component. In particular, we show that this category is reflective and coreflective in the category of $S$-cpo's, find the free and cofree functors, characterize products and coproducts. Furthermore, epimorphisms and monomorphisms in {$\bf Cpo_{Sep}$-$S$} are studied, and show that {$\bf Cpo_{Sep}$-$S$} is not cartesian closed.
Directed complete partially ordered set
Product
coproduct
cartesian closed
2015
07
01
21
42
https://cgasa.sbu.ac.ir/article_10031_d6b54d9be2f2a6c5a9c0ff061f40bc88.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2015
3
1
Order dense injectivity of $S$-posets
Leila
Shahbaz
In this paper, the notion of injectivity with respect to order dense embeddings in the category of $S$-posets, posets with a monotone action of a pomonoid $S$ on them, is studied. We give a criterion, like the Baer condition for injectivity of modules, or Skornjakov criterion for injectivity of $S$-sets, for the order dense injectivity. Also, we consider such injectivity for $S$ itself, and its order dense ideals. Further, we define and study some kinds of weak injectivity with respect to order dense embeddings, consider their relations with order dense injectivity. Also investigate if these kinds of injectivity are preserved or reflected by products, coproducts, and direct sums of$S$-posets.
regular monomorphism
order dense sub $S$-poset
order dense injective
2015
07
01
43
63
https://cgasa.sbu.ac.ir/article_10518_c47373537bc4095c9b7b11ef095abf14.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2015
3
1
$omega$-Operads of coendomorphisms and fractal $omega$-operads for higher structures
Camell
Kachour
In this article we introduce the notion of \textit{Fractal $\omega$-operad} emerging from a natural $\omega$-operad associated to any coglobular object in the category of higher operads in Batanin's sense, which in fact is a coendomorphism $\omega$-operads. We have in mind coglobular object of higher operads which algebras are kind of higher transformations. It follows that this natural $\omega$-operad acts on the globular object associated to these higher transformations. To construct the natural $\omega$-operad we introduce some general technology and give meaning to saying an $\omega$-operad possesses the \textit{fractal property}. If an $\omega$-operad $B^{0}_{P}$ has this property then one can define a globular object of all higher $B^{0}_{P}$-transformations and show that the globular object has a $B^{0}_{P}$-algebra structure.
Higher categories
higher operads
weak higher transformations
2015
07
01
65
88
https://cgasa.sbu.ac.ir/article_10527_391dbbec71f3cd9c77ef8d4d484a2ed9.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2015
3
1
Operads of higher transformations for globular sets and for higher magmas
Camell
Kachour
In this article we discuss examples of fractal $\omega$-operads. Thus we show that there is an $\omega$-operadic approach to explain existence of the globular set of globular sets\footnote{Globular sets are also called $\omega$-graphs by the French School.}, the reflexive globular set of reflexive globular sets, the $\omega$-magma of $\omega$-magmas, and also the reflexive $\omega$-magma of reflexive $\omega$-magmas. Thus, even though the existence of the globular set of globular sets is intuitively evident, many other higher structures which \textit{fractality} are less evident, could be described with the same technology, using fractal $\omega$-operads. We have in mind the non-trivial question of the existence of the weak $\omega$-category of the weak $\omega$-categories in the globular setting, which is described in \cite{kach-ir3} with the same technology up to a contractibility hypothesis.
Higher categories
higher operads
weak higher transformations
2015
07
01
89
111
https://cgasa.sbu.ac.ir/article_10528_b04f19db4ee999d77afc297225d3cf14.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2015
3
1
A cottage industry of lax extensions
Dirk
Hofmann
Gavin J.
Seal
In this work, we describe an adjunction between the comma category of Set-based monads under the V -powerset monad and the category of associative lax extensions of Set-based monads to the category of V -relations. In the process, we give a general construction of the Kleisli extension of a monad to the category of V-relations.
Monad
lax extension
quantale
enriched category
2015
07
01
113
151
https://cgasa.sbu.ac.ir/article_10709_6dda525bdadbecfac60152d5865b84f9.pdf
Categories and General Algebraic Structures with Applications
CGASA
2345-5853
2345-5853
2015
3
1
Persian Abstracts
2015
07
01
152
162
https://cgasa.sbu.ac.ir/article_10707_bd2ac56f873d9a78aca1d5cadb95d92a.pdf