APPLIED CATEGORICAL STRUCTURES 侧重于从范畴理论到数学、物理和计算机科学的结果、技术和思想的应用。这些包括拓扑和代数范畴的研究、表示论、代数几何、同调和同伦代数、派生和三角范畴、（几何）不变量的分类、数学物理中的分类研究、更高范畴的理论和应用、泛函分析中的分类研究，在连续阶理论和理论计算机科学中。此外，该杂志还跟踪新兴领域的发展，在这些领域中，分类方法的应用被证明是相关的。APPLIED CATEGORICAL STRUCTURES 发表经过仔细参考的研究论文和调查论文。它促进了在研究中使用分类方法的数学家和计算机科学家之间的交流并增加了新结果和新思想的传播。

The journal "Applied Categorical Structures" focuses on the applications of category theory in mathematics, physics, and computer science. This includes research on topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, classification of (geometric) invariants, categorical studies in mathematical physics, theories and applications of higher categories, and categorical studies in functional analysis, particularly in continuous order theory and theoretical computer science. Additionally, the journal tracks developments in emerging fields where the application of categorical methods has proven relevant. "Applied Categorical Structures" publishes rigorously peer-reviewed research papers and survey articles, fostering communication between mathematicians and computer scientists in the use of categorical methods in research and enhancing the dissemination of new results and ideas.

《Applied Categorical Structures》期刊专注于范畴理论在数学、物理和计算机科学中的应用，包括拓扑和代数范畴的研究、表示论、代数几何、同调和同伦代数、派生和三角范畴、（几何）不变量的分类、数学物理中的分类研究、更高范畴的理论与应用，以及泛函分析中的分类研究，涉及连续阶理论和理论计算机科学。此外，该期刊还关注新兴领域的发展，在这些领域中，分类方法的应用被证明是相关的。《Applied Categorical Structures》发表经过严格审查的研究论文和综述文章，促进数学家和计算机科学家之间在研究中使用分类方法的交流，并推动新结果和新思想的传播。

Applied Categorical Structures

Abstract Via the adjunction $$ - *\mathbbm {1} \dashv \mathcal V(\mathbbm {1},-) :\textsf {Span}({\mathcal {V}}) \rightarrow {\mathcal {V}} \text {-} \textsf {Mat} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>-</mml:mo> <mml:mrow/> <mml:mo>∗</mml:mo> <mml:mn>1</mml:mn> <mml:mo>⊣</mml:mo> <mml:mi>V</mml:mi> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mo>-</mml:mo> <mml:mo>)</mml:mo> <mml:mo>:</mml:mo> <mml:mi>Span</mml:mi> <mml:mo>(</mml:mo> <mml:mi>V</mml:mi> <mml:mo>)</mml:mo> <mml:mo>→</mml:mo> <mml:mi>V</mml:mi> <mml:mtext>-</mml:mtext> <mml:mi>Mat</mml:mi> </mml:mrow> </mml:math> and a cartesian monad T on an extensive category $$ {\mathcal {V}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>V</mml:mi> </mml:math> with finite limits, we construct an adjunction $$ - *\mathbbm {1} \dashv {\mathcal {V}}(\mathbbm {1},-) :\textsf {Cat}(T,{\mathcal {V}}) \rightarrow ({\overline{T}}, \mathcal V)\text{- }\textsf{Cat} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>-</mml:mo> <mml:mrow/> <mml:mo>∗</mml:mo> <mml:mn>1</mml:mn> <mml:mo>⊣</mml:mo> <mml:mi>V</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mo>-</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>:</mml:mo> <mml:mi>Cat</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>T</mml:mi> <mml:mo>,</mml:mo> <mml:mi>V</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>→</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>,</mml:mo> <mml:mi>V</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mtext>-</mml:mtext> <mml:mspace/> <mml:mi>Cat</mml:mi> </mml:mrow> </mml:math> between categories of generalized enriched multicategories and generalized internal multicategories, provided the monad T satisfies a suitable property, which holds for several examples. We verify, moreover, that the left adjoint is fully faithful, and preserves pullbacks, provided that the copower functor $$ - *\mathbbm {1} :\textsf {Set} \rightarrow {\mathcal {V}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>-</mml:mo> <mml:mrow/> <mml:mo>∗</mml:mo> <mml:mn>1</mml:mn> <mml:mo>:</mml:mo> <mml:mi>Set</mml:mi> <mml:mo>→</mml:mo> <mml:mi>V</mml:mi> </mml:mrow> </mml:math> is fully faithful. We also apply this result to study descent theory of generalized enriched multicategorical structures. These results are built upon the study of base-change for generalized multicategories, which, in turn, was carried out in the context of categories of horizontal lax algebras arising out of a monad in a suitable 2-category of pseudodouble categories.

Rui Prezado

Fernando Lucatelli Nunes

Generalized Multicategories: Change-of-Base, Embedding, and Descent

广义多范畴：基变换、嵌入与下降

Abstract The approximation classes of modules that arise as components of cotorsion pairs are tied up by Salce’s duality. Here we consider general approximation classes of modules and investigate possibilities of dualization in dependence on closure properties of these classes. While some proofs are easily dualized, other dualizations require large cardinal principles, and some fail in ZFC, with counterexamples provided by classes of $$\aleph _1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ℵ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> -projective modules over non-perfect rings. For example, we show that the statement “each covering class of modules closed under homomorphic images is of the form $${\mathrm{Gen\,}}(M)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mi>Gen</mml:mi> <mml:mspace/> </mml:mrow> <mml:mo>(</mml:mo> <mml:mi>M</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> for a module M ” is equivalent to Vopěnka’s Principle.

Asmae Ben Yassine

Jan Trlifaj

Dualizations of Approximations, $$\aleph _1$$-Projectivity, and Vopěnka’s Principles

近似、$$\aleph _1$$-射影性和沃佩纳卡原理的对偶化

Abstract Matrix properties are a type of property of categories which includes the ones of being Mal’tsev, arithmetical, majority, unital, strongly unital, and subtractive. Recently, an algorithm has been developed to determine implications $$\textrm{M}\Rightarrow _{\textrm{lex}_*}\textrm{N}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>M</mml:mtext> <mml:mmultiscripts> <mml:mo>⇒</mml:mo> <mml:mmultiscripts> <mml:mtext>lex</mml:mtext> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> <mml:mrow/> </mml:mmultiscripts> <mml:mrow/> </mml:mmultiscripts> <mml:mtext>N</mml:mtext> </mml:mrow> </mml:math> between them. We show here that this algorithm reduces to constructing a partial term corresponding to $$\textrm{N}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>N</mml:mtext> </mml:math> from a partial term corresponding to $$\textrm{M}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>M</mml:mtext> </mml:math> . Moreover, we prove that this is further equivalent to the corresponding implication between the weak versions of these properties, i.e., the one where only strong monomorphisms are considered instead of all monomorphisms.

Michael Hoefnagel

Pierre-Alain Jacqmin

Partial Algebras and Implications of (Weak) Matrix Properties

偏代数与（弱）矩阵性质的含义

Amar Hadzihasanovic

Diana Kessler

Acyclicity Conditions on Pasting Diagrams

粘贴图上的无环性条件

Abstract Inspired by some properties of the (dual of the) category of 2-nilpotent groups, we introduce the notion of 2-unital and 2-Mal’tsev categories which, in some sense, generalises the notion of unital and Mal’tsev categories, and we characterise their varietal occurrences. This is actually the first step of an inductive process which we begin to unfold.

短名	Appl. Categor. Struct.
Journal Impact	0.63
国际分区	MATHEMATICS(Q3)
期刊索引	SCI Q3中科院 4 区

ISSN	0927-2852, 1572-9095
h-index	32
国内分区	数学(4区)数学数学(4区)

涉及主题	数学计算机科学纯数学离散数学组合数学程序设计语言算法物理计算理论域代数上的工程类化学哲学生物数学分析量子力学
出版信息	出版商: Springer Netherlands，出版周期: Bimonthly，期刊类型: journal，开源期刊: 否
基本数据	创刊年份: 1993，原创研究文献占比: 100.00%，自引率:16.70%， Gold OA占比: 23.77%
平均审稿周期	网友分享经验：>12周，或约稿
平均录用比例	网友分享经验：容易

Applied Categorical Structures

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Generalized Multicategories: Change-of-Base, Embedding, and Descent

Dualizations of Approximations, $$\aleph _1$$-Projectivity, and Vopěnka’s Principles

Partial Algebras and Implications of (Weak) Matrix Properties

Acyclicity Conditions on Pasting Diagrams

On n-unital and n-Mal’tsev categories

Dualizations of Approximations, $$\aleph _1$$-Projectivity, and Vopěnka’s Principles

Generalized Multicategories: Change-of-Base, Embedding, and Descent

Partial Algebras and Implications of (Weak) Matrix Properties

A Note on the Smash Product and Regular Associativity

Acyclicity Conditions on Pasting Diagrams