Pub Date : 2018-03-01DOI: 10.1142/9789813231078_0006
M. Grandis
{"title":"Applications in Topology and Algebraic Topology","authors":"M. Grandis","doi":"10.1142/9789813231078_0006","DOIUrl":"https://doi.org/10.1142/9789813231078_0006","url":null,"abstract":"","PeriodicalId":188337,"journal":{"name":"Category Theory and Applications","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124553307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-03-01DOI: 10.1142/9789813231078_0008
M. Grandis
{"title":"Hints at higher dimensional category theory","authors":"M. Grandis","doi":"10.1142/9789813231078_0008","DOIUrl":"https://doi.org/10.1142/9789813231078_0008","url":null,"abstract":"","PeriodicalId":188337,"journal":{"name":"Category Theory and Applications","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115056401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-03-01DOI: 10.1142/9789813231078_0007
M. Grandis
{"title":"Applications in Homological Algebra","authors":"M. Grandis","doi":"10.1142/9789813231078_0007","DOIUrl":"https://doi.org/10.1142/9789813231078_0007","url":null,"abstract":"","PeriodicalId":188337,"journal":{"name":"Category Theory and Applications","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114462998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-03-01DOI: 10.1142/9789813231078_0004
M. Grandis
{"title":"Adjunctions and monads","authors":"M. Grandis","doi":"10.1142/9789813231078_0004","DOIUrl":"https://doi.org/10.1142/9789813231078_0004","url":null,"abstract":"","PeriodicalId":188337,"journal":{"name":"Category Theory and Applications","volume":"150 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132379566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-03-07DOI: 10.1002/9781118619988.CH14
H. Bourlès
{"title":"Solutions of the exercises","authors":"H. Bourlès","doi":"10.1002/9781118619988.CH14","DOIUrl":"https://doi.org/10.1002/9781118619988.CH14","url":null,"abstract":"","PeriodicalId":188337,"journal":{"name":"Category Theory and Applications","volume":"113 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123998672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Applications in Algebra","authors":"G. Birkhoff","doi":"10.1090/coll/025/07","DOIUrl":"https://doi.org/10.1090/coll/025/07","url":null,"abstract":"","PeriodicalId":188337,"journal":{"name":"Category Theory and Applications","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1940-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122942266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1142/9789811236099_bmatter
{"title":"BACK MATTER","authors":"","doi":"10.1142/9789811236099_bmatter","DOIUrl":"https://doi.org/10.1142/9789811236099_bmatter","url":null,"abstract":"","PeriodicalId":188337,"journal":{"name":"Category Theory and Applications","volume":"172 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122990212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1142/9789811236099_0003
Jon P. May
Let D be a small category and let C be any category. A D-shaped diagram in C is a functor F : D −→ C . A morphism F −→ F ′ of D-shaped diagrams is a natural transformation, and we have the category D [C ] of D-shaped diagrams in C . Any object C of C determines the constant diagram C that sends each object of D to C and sends each morphism of D to the identity morphism of C. The colimit, colimF , of a D-shaped diagram F is an object of C together with a morphism of diagrams ι : F −→ colim F that is initial among all such morphisms. This means that if η : F −→ A is a morphism of diagrams, then there is a unique map η̃ : colim F −→ A in C such that η̃ ◦ ι = η. Diagrammatically, this property is expressed by the assertion that, for each map d : D −→ D in D , we have a commutative diagram
{"title":"Limits and colimits","authors":"Jon P. May","doi":"10.1142/9789811236099_0003","DOIUrl":"https://doi.org/10.1142/9789811236099_0003","url":null,"abstract":"Let D be a small category and let C be any category. A D-shaped diagram in C is a functor F : D −→ C . A morphism F −→ F ′ of D-shaped diagrams is a natural transformation, and we have the category D [C ] of D-shaped diagrams in C . Any object C of C determines the constant diagram C that sends each object of D to C and sends each morphism of D to the identity morphism of C. The colimit, colimF , of a D-shaped diagram F is an object of C together with a morphism of diagrams ι : F −→ colim F that is initial among all such morphisms. This means that if η : F −→ A is a morphism of diagrams, then there is a unique map η̃ : colim F −→ A in C such that η̃ ◦ ι = η. Diagrammatically, this property is expressed by the assertion that, for each map d : D −→ D in D , we have a commutative diagram","PeriodicalId":188337,"journal":{"name":"Category Theory and Applications","volume":"133 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122886840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1142/9789811236099_fmatter
{"title":"FRONT MATTER","authors":"","doi":"10.1142/9789811236099_fmatter","DOIUrl":"https://doi.org/10.1142/9789811236099_fmatter","url":null,"abstract":"","PeriodicalId":188337,"journal":{"name":"Category Theory and Applications","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117051813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1007/978-1-4612-9839-7_2
S. Lane
{"title":"Categories, functors and natural transformations","authors":"S. Lane","doi":"10.1007/978-1-4612-9839-7_2","DOIUrl":"https://doi.org/10.1007/978-1-4612-9839-7_2","url":null,"abstract":"","PeriodicalId":188337,"journal":{"name":"Category Theory and Applications","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123322838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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