Applied Categorical Structures最新文献

A Characterization of Differential Bundles in Tangent Categories 切线范畴中微分束的特征

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2024-09-16 DOI: 10.1007/s10485-024-09786-9

Michael Ching

引用次数: 0

Diagrammatics for Comodule Monads 组合单子图解法

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2024-08-29 DOI: 10.1007/s10485-024-09778-9

Sebastian Halbig, Tony Zorman

引用次数: 0

Functorial Polar Functions in Compact Normal Joinfit Frames 紧凑法向 Joinfit 框架中的扇形极坐标函数

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2024-08-23 DOI: 10.1007/s10485-024-09783-y

Ricardo E. Carrera

{"title":"Functorial Polar Functions in Compact Normal Joinfit Frames","authors":"Ricardo E. Carrera","doi":"10.1007/s10485-024-09783-y","DOIUrl":"https://doi.org/10.1007/s10485-024-09783-y","url":null,"abstract":"(mathfrak {KNJ}) is the category of compact normal joinfit frames and frame homomorphisms. (mathcal {P}F) is the complete boolean algebra of polars of the frame F. A function (mathfrak {X}) that assigns to each (F in mathfrak {KNJ}) a subalgebra (mathfrak {X}(F)) of (mathcal {P}F) that contains the complemented elements of F is a polar function. A polar function (mathfrak {X}) is invariant (resp., functorial) if whenever (phi : F longrightarrow H in mathfrak {KNJ}) is (mathcal {P})-essential (resp., skeletal) and (p in mathfrak {X}(F)), then (phi (p)^{perp perp } in mathfrak {X}(H)). (phi : F longrightarrow H in mathfrak {KNJ}) is (mathfrak {X})-splitting if (phi ) is (mathcal {P})-essential and whenever (p in mathfrak {X}(F)), then (phi (p)^{perp perp }) is complemented in H. (F in mathfrak {KNJ}) is (mathfrak {X})-projectable means that every (p in mathfrak {X}(F)) is complemented. For a polar function (mathfrak {X}) and (F in mathfrak {KNJ}), we construct the least (mathfrak {X})-splitting frame of F. Moreover, we prove that if (mathfrak {X}) is a functorial polar function, then the class of (mathfrak {X})-projectable frames is a (mathcal {P})-essential monoreflective subcategory of (mathfrak {KNJS}), the category of (mathfrak {KNJ})-objects and skeletal maps (the case (mathfrak {X}= mathcal {P}) is the result from Martínez and Zenk, which states that the class of strongly projectable (mathfrak {KNJ})-objects is a reflective subcategory of (mathfrak {KNJS})).","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Differential Bundles of the Geometric Tangent Category of an Operad 算子几何切线范畴的差分束

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2024-08-19 DOI: 10.1007/s10485-024-09771-2

Marcello Lanfranchi

{"title":"The Differential Bundles of the Geometric Tangent Category of an Operad","authors":"Marcello Lanfranchi","doi":"10.1007/s10485-024-09771-2","DOIUrl":"https://doi.org/10.1007/s10485-024-09771-2","url":null,"abstract":"Affine schemes can be understood as objects of the opposite of the category of commutative and unital algebras. Similarly, (mathscr {P})-affine schemes can be defined as objects of the opposite of the category of algebras over an operad (mathscr {P}). An example is the opposite of the category of associative algebras. The category of operadic schemes of an operad carries a canonical tangent structure. This paper aims to initiate the study of the geometry of operadic affine schemes via this tangent category. For example, we expect the tangent structure over the opposite of the category of associative algebras to describe algebraic non-commutative geometry. In order to initiate such a program, the first step is to classify differential bundles, which are the analogs of vector bundles for differential geometry. In this paper, we prove that the tangent category of affine schemes of the enveloping operad (mathscr {P}^{(A)}) over a (mathscr {P})-affine scheme A is precisely the slice tangent category over A of (mathscr {P})-affine schemes. We are going to employ this result to show that differential bundles over a (mathscr {P})-affine scheme A are precisely A-modules in the operadic sense.","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Semiseparable Functors and Conditions up to Retracts 半可分函数和条件直至撤回

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2024-08-13 DOI: 10.1007/s10485-024-09782-z

Alessandro Ardizzoni, Lucrezia Bottegoni

引用次数: 0

Homotopy Quotients and Comodules of Supercommutative Hopf Algebras 超交换霍普夫布拉斯的同调对数和协元

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2024-08-12 DOI: 10.1007/s10485-024-09781-0

Thorsten Heidersdorf, Rainer Weissauer

{"title":"Homotopy Quotients and Comodules of Supercommutative Hopf Algebras","authors":"Thorsten Heidersdorf, Rainer Weissauer","doi":"10.1007/s10485-024-09781-0","DOIUrl":"https://doi.org/10.1007/s10485-024-09781-0","url":null,"abstract":"We study model structures on the category of comodules of a supercommutative Hopf algebra A over fields of characteristic 0. Given a graded Hopf algebra quotient (A rightarrow B) satisfying some finiteness conditions, the Frobenius tensor category ({mathcal {D}}) of graded B-comodules with its stable model structure induces a monoidal model structure on ({mathcal {C}}). We consider the corresponding homotopy quotient (gamma : {mathcal {C}} rightarrow Ho {mathcal {C}}) and the induced quotient ({mathcal {T}} rightarrow Ho {mathcal {T}}) for the tensor category ({mathcal {T}}) of finite dimensional A-comodules. Under some mild conditions we prove vanishing and finiteness theorems for morphisms in (Ho {mathcal {T}}). We apply these results in the Rep(GL(m|n))-case and study its homotopy category (Ho {mathcal {T}}) associated to the parabolic subgroup of upper triangular block matrices. We construct cofibrant replacements and show that the quotient of (Ho{mathcal {T}}) by the negligible morphisms is again the representation category of a supergroup scheme.","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Topological Quantum Field Theories and Homotopy Cobordisms 拓扑量子场论与同调共线性

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2024-07-31 DOI: 10.1007/s10485-024-09776-x

Fiona Torzewska

{"title":"Topological Quantum Field Theories and Homotopy Cobordisms","authors":"Fiona Torzewska","doi":"10.1007/s10485-024-09776-x","DOIUrl":"https://doi.org/10.1007/s10485-024-09776-x","url":null,"abstract":"We construct a category ({textrm{HomCob}}) whose objects are homotopically 1-finitely generated topological spaces, and whose morphisms are cofibrant cospans. Given a manifold submanifold pair (M, A), we prove that there exists functors into ({textrm{HomCob}}) from the full subgroupoid of the mapping class groupoid (textrm{MCG}_{M}^{A}), and from the full subgroupoid of the motion groupoid (textrm{Mot}_{M}^{A}), whose objects are homotopically 1-finitely generated. We also construct a family of functors ({textsf{Z}}_G:{textrm{HomCob}}rightarrow {textbf{Vect}}), one for each finite group G. These generalise topological quantum field theories previously constructed by Yetter, and an untwisted version of Dijkgraaf–Witten. Given a space X, we prove that ({textsf{Z}}_G(X)) can be expressed as the ({mathbb {C}})-vector space with basis natural transformation classes of maps from (pi (X,X_0)) to G for some finite representative set of points (X_0subset X), demonstrating that ({textsf{Z}}_G) is explicitly calculable.","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141868290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Presenting the Sierpinski Gasket in Various Categories of Metric Spaces 在各类度量空间中呈现西尔平斯基垫圈

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2024-07-30 DOI: 10.1007/s10485-024-09773-0

Jayampathy Ratnayake, Annanthakrishna Manokaran, Romaine Jayewardene, Victoria Noquez, Lawrence S. Moss

引用次数: 0

Locally Coherent Exact Categories 局部相干的精确类别

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2024-07-26 DOI: 10.1007/s10485-024-09780-1

Leonid Positselski

引用次数: 0

Universal Finite Functorial Semi-norms 通用有限函数半规范

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2024-07-19 DOI: 10.1007/s10485-024-09777-w

Clara Löh, Johannes Witzig

引用次数: 0