{"title":"内部丰富类别","authors":"Enrico Ghiorzi","doi":"10.1007/s10485-022-09678-w","DOIUrl":null,"url":null,"abstract":"<div><p>We introduce the theory of enrichment over an internal monoidal category as a common generalization of both the standard theories of enriched and internal categories. Then, we contextualize the new notion by comparing it to another known generalization of enrichment: that of enrichment for indexed categories. It turns out that the two notions are closely related.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2022-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-022-09678-w.pdf","citationCount":"0","resultStr":"{\"title\":\"Internal Enriched Categories\",\"authors\":\"Enrico Ghiorzi\",\"doi\":\"10.1007/s10485-022-09678-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We introduce the theory of enrichment over an internal monoidal category as a common generalization of both the standard theories of enriched and internal categories. Then, we contextualize the new notion by comparing it to another known generalization of enrichment: that of enrichment for indexed categories. It turns out that the two notions are closely related.</p></div>\",\"PeriodicalId\":7952,\"journal\":{\"name\":\"Applied Categorical Structures\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2022-04-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10485-022-09678-w.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Categorical Structures\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10485-022-09678-w\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Categorical Structures","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10485-022-09678-w","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We introduce the theory of enrichment over an internal monoidal category as a common generalization of both the standard theories of enriched and internal categories. Then, we contextualize the new notion by comparing it to another known generalization of enrichment: that of enrichment for indexed categories. It turns out that the two notions are closely related.
期刊介绍：
Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, physics and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorification of (geometric) invariants, categorical investigations in mathematical physics, higher category theory and applications, categorical investigations in functional analysis, in continuous order theory and in theoretical computer science. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant.
Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.
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