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

G. S. H. Cruttwell

Jean-Simon Pacaud Lemay

Elias Vandenberg

A Tangent Category Perspective on Connections in Algebraic Geometry

代数几何中联络的切范畴视角

Abstract We present a geometrically oriented classification theory for non-Abelian extensions of groupoids generalizing the classification theory for Abelian extensions of groupoids by Westman as well as the familiar classification theory for non-Abelian extensions of groups by Schreier and Eilenberg-MacLane. As an application of our techniques we demonstrate that each extension of groupoids $${\mathcal {N}}\rightarrow {\mathcal {E}}\rightarrow {\mathcal {G}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>→</mml:mo> <mml:mi>E</mml:mi> <mml:mo>→</mml:mo> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> gives rise to a groupoid crossed product of $${\mathcal {G}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>G</mml:mi> </mml:math> by the groupoid ring of $${\mathcal {N}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> which recovers the groupoid ring of $${\mathcal {E}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>E</mml:mi> </mml:math> up to isomorphism. Furthermore, we make the somewhat surprising observation that our classification methods naturally transfer to the class of groupoid crossed products, thus providing a classification theory for this class of rings. Our study is motivated by the search for natural examples of groupoid crossed products.

Natã Machado

Johan Öinert

Stefan Wagner

Non-Abelian Extensions of Groupoids and Their Groupoid Rings

群胚的非阿贝尔扩张及其群胚环

Abstract We develop a 2-dimensional version of accessibility and presentability compatible with the formalism of flat pseudofunctors. First we give prerequisites on the different notions of 2-dimensional colimits, filteredness and cofinality; in particular we show that $$\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>σ</mml:mi> </mml:math> - filteredness and bifilteredness are actually equivalent in practice for our purposes. Then, we define bi-accessible and bipresentable 2-categories in terms of bicompact objects and bifiltered bicolimits. We then characterize them as categories of flat pseudofunctors . We also prove a bi-accessible right bi-adjoint functor theorem and deduce a 2-dimensional Gabriel-Ulmer duality relating small bilex 2-categories and finitely bipresentable 2-categories. Finally, we show that 2-categories of pseudo-algebras of finitary 2-monads on $$\textbf{Cat}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Cat</mml:mi> </mml:math> are finitely bipresentable, which in particular captures the case of $$\textbf{Lex}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Lex</mml:mi> </mml:math> , the 2-category of small lex categories. Invoking the technology of lex-colimits , we prove further that several 2-categories arising in categorical logic ( Reg, Ex, Coh, Ext, Adh, Pretop ) are also finitely bipresentable.

Ivan Di Liberti

Axel Osmond

Bi-accessible and Bipresentable 2-Categories

双可及与双可表的2-范畴

Abstract Let $${{\mathcal {O}}}\rightarrow {\text {BM}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>→</mml:mo> <mml:mtext>BM</mml:mtext> </mml:mrow> </mml:math> be a $${\text {BM}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>BM</mml:mtext> </mml:math> -operad that exhibits an $$\infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>∞</mml:mi> </mml:math> -category $${{\mathcal {D}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>D</mml:mi> </mml:math> as weakly bitensored over non-symmetric $$\infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>∞</mml:mi> </mml:math> -operads $${{\mathcal {V}}}\rightarrow \text {Ass }, {{\mathcal {W}}}\rightarrow \text {Ass }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>V</mml:mi> <mml:mo>→</mml:mo> <mml:mtext>Ass</mml:mtext> <mml:mspace/> <mml:mo>,</mml:mo> <mml:mi>W</mml:mi> <mml:mo>→</mml:mo> <mml:mtext>Ass</mml:mtext> <mml:mspace/> </mml:mrow> </mml:math> and $${{\mathcal {C}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> a $${{\mathcal {V}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>V</mml:mi> </mml:math> -enriched $$\infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>∞</mml:mi> </mml:math> -precategory. We construct an equivalence $$\begin{aligned} \text {Fun}_{\text {Hin}}^{{\mathcal {V}}}({{\mathcal {C}}},{{\mathcal {D}}}) \simeq \text {Fun}^{{\mathcal {V}}}({{\mathcal {C}}},{{\mathcal {D}}}) \end{aligned}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtable> <mml:mtr> <mml:mtd> <mml:mrow> <mml:msubsup> <mml:mtext>Fun</mml:mtext> <mml:mrow> <mml:mtext>Hin</mml:mtext> </mml:mrow> <mml:mi>V</mml:mi> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>C</mml:mi> <mml:mo>,</mml:mo> <mml:mi>D</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>≃</mml:mo> <mml:msup> <mml:mtext>Fun</mml:mtext> <mml:mi>V</mml:mi> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>C</mml:mi> <mml:mo>,</mml:mo> <mml:mi>D</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:mtd> </mml:mtr> </mml:mtable> </mml:mrow> </mml:math> of $$\infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>∞</mml:mi> </mml:math> -categories weakly right tensored over $${{\mathcal {W}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>W</mml:mi> </mml:math> between Hinich’s construction of $${{\mathcal {V}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>V</mml:mi> </mml:math> -enriched functors of Hinich (Adv Math 367:107129, 2020) and our construction of $${{\mathcal {V}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>V</mml:mi> </mml:math> -enriched functors of Heine (Adv Math 417:108941, 2023).

Abbreviation	Appl. Categor. Struct.
Journal Impact	0.63
Quartiles(Global)	MATHEMATICS(Q3)

ISSN	0927-2852, 1572-9095
h-index	32

Publication Information	Publisher: Springer Netherlands，Publishing cycle: Bimonthly，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 1993，Proportion of original research papers: 100.00%，Self Citation Rate:16.70%， Gold OA Rate: 23.77%
Average review cycle	网友分享经验：>12周，或约稿
Average recruitment ratio	网友分享经验：容易

Applied Categorical Structures

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A Tangent Category Perspective on Connections in Algebraic Geometry

Non-Abelian Extensions of Groupoids and Their Groupoid Rings

Bi-accessible and Bipresentable 2-Categories

An Equivalence Between Two Models of $$\infty $$-Categories of Enriched Presheaves

Operad Structures on the Species Composition of Two Operads

Non-Abelian Extensions of Groupoids and Their Groupoid Rings

A Tangent Category Perspective on Connections in Algebraic Geometry

Bi-accessible and Bipresentable 2-Categories

An Equivalence Between Two Models of $$\infty $$-Categories of Enriched Presheaves

Operad Structures on the Species Composition of Two Operads