Applied Categorical Structures最新文献_第8页

Inner Automorphisms of Presheaves of Groups 群的Presheaves的内自同构

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-04-08 DOI: 10.1007/s10485-023-09720-5

Jason Parker

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引用次数: 3

Free gs-Monoidal Categories and Free Markov Categories 自由gs-一元范畴和自由马尔可夫范畴

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-04-08 DOI: 10.1007/s10485-023-09717-0

Tobias Fritz, Wendong Liang

{"title":"Free gs-Monoidal Categories and Free Markov Categories","authors":"Tobias Fritz, Wendong Liang","doi":"10.1007/s10485-023-09717-0","DOIUrl":"10.1007/s10485-023-09717-0","url":null,"abstract":"<div>Categorical probability has recently seen significant advances through the formalism of Markov categories, within which several classical theorems have been proven in entirely abstract categorical terms. Closely related to Markov categories are gs-monoidal categories, also known as CD categories. These omit a condition that implements the normalization of probability. Extending work of Corradini and Gadducci, we construct free gs-monoidal and free Markov categories generated by a collection of morphisms of arbitrary arity and coarity. For free gs-monoidal categories, this comes in the form of an explicit combinatorial description of their morphisms as structured cospans of labeled hypergraphs. These can be thought of as a formalization of gs-monoidal string diagrams ((=)term graphs) as a combinatorial data structure. We formulate the appropriate 2-categorical universal property based on ideas of Walters and prove that our categories satisfy it. We expect our free categories to be relevant for computer implementations and we also argue that they can be used as statistical causal models generalizing Bayesian networks.\u0000</div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09717-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44975154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 19

Distributive Laws for Relative Monads 相对单子的分配律

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-04-05 DOI: 10.1007/s10485-023-09716-1

Gabriele Lobbia

引用次数: 1

Rings and Modules in Kan Spectra Kan光谱中的环和模

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-04-04 DOI: 10.1007/s10485-023-09719-y

R. Chen, I. Kriz, A. Pultr

引用次数: 0

Clifford’s Theorem for Orbit Categories 轨道范畴的Clifford定理

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-04-03 DOI: 10.1007/s10485-023-09721-4

Alexander Zimmermann

引用次数: 0

Locally Type (text {FP}_{{varvec{n}}}) and ({varvec{n}})-Coherent Categories 本地输入(text {FP}_{{varvec{n}}})和({varvec{n}}) -连贯类别

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-03-27 DOI: 10.1007/s10485-023-09709-0

Daniel Bravo, James Gillespie, Marco A. Pérez

{"title":"Locally Type (text {FP}_{{varvec{n}}}) and ({varvec{n}})-Coherent Categories","authors":"Daniel Bravo, James Gillespie, Marco A. Pérez","doi":"10.1007/s10485-023-09709-0","DOIUrl":"10.1007/s10485-023-09709-0","url":null,"abstract":"<div>We study finiteness conditions in Grothendieck categories by introducing the concepts of objects of type (textrm{FP}_n) and studying their closure properties with respect to short exact sequences. This allows us to propose a notion of locally type (textrm{FP}_n) categories as a generalization of locally finitely generated and locally finitely presented categories. We also define and study the injective objects that are Ext-orthogonal to the class of objects of type (textrm{FP}_n), called (textrm{FP}_n)-injective objects, which will be the right half of a complete cotorsion pair. As a generalization of the category of modules over an n-coherent ring, we present the concept of n-coherent categories, which also recovers the notions of locally noetherian and locally coherent categories for (n = 0, 1). Such categories will provide a setting in which the (textrm{FP}_n)-injective cotorsion pair is hereditary, and where it is possible to construct (pre)covers by (textrm{FP}_n)-injective objects.</div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09709-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50050367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Locally Type $$text {FP}_{{varvec{n}}}$$ FP n and 本地键入$$text{FP}_｛varvec｛n｝｝$FP n和

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-03-27 DOI: 10.1007/s10485-023-09709-0

D. Bravo, James Gillespie, Marco A. Pérez

引用次数: 0

Higher Auslander’s defect and classifying substructures of (varvec{n})-exangulated categories 高等澳洲人的缺陷与(varvec{n}) -膨化分类的分类子结构

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-03-20 DOI: 10.1007/s10485-023-09713-4

Jiangsheng Hu, Yajun Ma, Dongdong Zhang, Panyue Zhou

引用次数: 0

Closed and Open Maps for Partial Frames 部分帧的封闭和开放映射

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-03-15 DOI: 10.1007/s10485-023-09712-5

John Frith, Anneliese Schauerte

{"title":"Closed and Open Maps for Partial Frames","authors":"John Frith, Anneliese Schauerte","doi":"10.1007/s10485-023-09712-5","DOIUrl":"10.1007/s10485-023-09712-5","url":null,"abstract":"<div>This paper concerns the notions of closed and open maps in the setting of partial frames, which, in contrast to full frames, do not necessarily have all joins. Examples of these include bounded distributive lattices, (sigma )- and (kappa )-frames and full frames. We define closed and open maps using geometrically intuitively appealing conditions involving preservation of closed, respectively open, congruences under certain maps. We then characterize them in terms of algebraic identities involving adjoints. We note that partial frame maps need have neither right nor left adjoints whereas frame maps of course always have right adjoints. The embedding of a partial frame in either its free frame or its congruence frame has proved illuminating and useful. We consider the conditions under which these embeddings are closed, open or skeletal. We then look at preservation and reflection of closed or open maps under the functors providing the free frame or the congruence frame. Points arise naturally in the construction of the spectrum functor for partial frames to partial spaces. They may be viewed as maps from the given partial frame to the 2-chain or as certain kinds of filters; using the former description we consider closed and open points. Any point of a partial frame extends naturally to a point on its free frame and a point on its congruence frame; we consider the closedness or openness of these.</div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-023-09712-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50029789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Closed and Open Maps for Partial Frames 部分帧的封闭和开放映射

IF 0.6 4区数学

Applied Categorical Structures Pub Date : 2023-03-15 DOI: 10.1007/s10485-023-09712-5

J. Frith, A. Schauerte

引用次数: 0