Triangulated Structures Induced by Triangle Functors
Given a triangle functor F : A → B , the authors introduce the half image hIm F , which is an additive category closely related to F . If F is full or faithful, then hIm F admits a natural triangulated structure. However, in general, one can not expect that hIm F has a natural triangulated structure...
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| Veröffentlicht in: | Chinese annals of mathematics. Serie B 2019, Vol.40 (1), p.55-64 |
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| container_title | Chinese annals of mathematics. Serie B |
| container_volume | 40 |
| creator | Zhao, Zhibing Du, Xianneng Bao, Yanhong |
| description | Given a triangle functor
F
:
A
→
B
, the authors introduce the half image hIm
F
, which is an additive category closely related to
F
. If
F
is full or faithful, then hIm
F
admits a natural triangulated structure. However, in general, one can not expect that hIm
F
has a natural triangulated structure. The aim of this paper is to prove that hIm
F
admits a natural triangulated structure if and only if
F
satisfies the condition (SM). If this is the case, hIm
F
is triangle-equivalent to the Verdier quotient
A
/Ker
F
. |
| doi_str_mv | 10.1007/s11401-018-0117-1 |
| format | Article |
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F
:
A
→
B
, the authors introduce the half image hIm
F
, which is an additive category closely related to
F
. If
F
is full or faithful, then hIm
F
admits a natural triangulated structure. However, in general, one can not expect that hIm
F
has a natural triangulated structure. The aim of this paper is to prove that hIm
F
admits a natural triangulated structure if and only if
F
satisfies the condition (SM). If this is the case, hIm
F
is triangle-equivalent to the Verdier quotient
A
/Ker
F
.</description><identifier>ISSN: 0252-9599</identifier><identifier>EISSN: 1860-6261</identifier><identifier>DOI: 10.1007/s11401-018-0117-1</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applications of Mathematics ; Kerf ; Mathematics ; Mathematics and Statistics</subject><ispartof>Chinese annals of mathematics. Serie B, 2019, Vol.40 (1), p.55-64</ispartof><rights>Fudan University and Springer-Verlag GmbH Germany, part of Springer Nature 2019</rights><rights>Copyright Springer Science & Business Media 2019</rights><rights>Copyright © Wanfang Data Co. Ltd. All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c300t-f600baf3f37743dc7e5c758cf411b7a5e44bdee701830e21013632bdf1185fe3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttp://www.wanfangdata.com.cn/images/PeriodicalImages/sxnk-e/sxnk-e.jpg</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11401-018-0117-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11401-018-0117-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>315,781,785,4025,27928,27929,27930,41493,42562,51324</link.rule.ids></links><search><creatorcontrib>Zhao, Zhibing</creatorcontrib><creatorcontrib>Du, Xianneng</creatorcontrib><creatorcontrib>Bao, Yanhong</creatorcontrib><title>Triangulated Structures Induced by Triangle Functors</title><title>Chinese annals of mathematics. Serie B</title><addtitle>Chin. Ann. Math. Ser. B</addtitle><description>Given a triangle functor
F
:
A
→
B
, the authors introduce the half image hIm
F
, which is an additive category closely related to
F
. If
F
is full or faithful, then hIm
F
admits a natural triangulated structure. However, in general, one can not expect that hIm
F
has a natural triangulated structure. The aim of this paper is to prove that hIm
F
admits a natural triangulated structure if and only if
F
satisfies the condition (SM). If this is the case, hIm
F
is triangle-equivalent to the Verdier quotient
A
/Ker
F
.</description><subject>Applications of Mathematics</subject><subject>Kerf</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0252-9599</issn><issn>1860-6261</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kE9LAzEQxYMoWKsfwNuCB0_RmfzZ7B6lWC0UPNh72M0mpbVma7JB--1NWaEnD8PA8Hszbx4htwgPCKAeI6IApIBVLlQUz8gEqxJoyUo8JxNgktFa1vUluYpxC4BCSZgQsQqbxq_TrhlsV7wPIZkhBRuLhe-SyaP2UIzIzhbz5M3Qh3hNLlyzi_bmr0_Jav68mr3S5dvLYva0pIYDDNSVAG3juONKCd4ZZaVRsjJOILaqkVaItrNWZdMcLENAXnLWdg6xks7yKbkf13433mUHetun4PNBHX_8h7YMsIb8Pc_k3UjuQ_-VbBxOKENZlSxng5nCkTKhjzFYp_dh89mEg0bQxxT1mKLOhvQxRX3UsFETM-vXNpw2_y_6Bdlxcuw</recordid><startdate>2019</startdate><enddate>2019</enddate><creator>Zhao, Zhibing</creator><creator>Du, Xianneng</creator><creator>Bao, Yanhong</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><general>School of Mathematical Sciences,Anhui University,Hefei 230601,China</general><scope>AAYXX</scope><scope>CITATION</scope><scope>2B.</scope><scope>4A8</scope><scope>92I</scope><scope>93N</scope><scope>PSX</scope><scope>TCJ</scope></search><sort><creationdate>2019</creationdate><title>Triangulated Structures Induced by Triangle Functors</title><author>Zhao, Zhibing ; Du, Xianneng ; Bao, Yanhong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c300t-f600baf3f37743dc7e5c758cf411b7a5e44bdee701830e21013632bdf1185fe3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Applications of Mathematics</topic><topic>Kerf</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhao, Zhibing</creatorcontrib><creatorcontrib>Du, Xianneng</creatorcontrib><creatorcontrib>Bao, Yanhong</creatorcontrib><collection>CrossRef</collection><collection>Wanfang Data Journals - Hong Kong</collection><collection>WANFANG Data Centre</collection><collection>Wanfang Data Journals</collection><collection>万方数据期刊 - 香港版</collection><collection>China Online Journals (COJ)</collection><collection>China Online Journals (COJ)</collection><jtitle>Chinese annals of mathematics. Serie B</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhao, Zhibing</au><au>Du, Xianneng</au><au>Bao, Yanhong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Triangulated Structures Induced by Triangle Functors</atitle><jtitle>Chinese annals of mathematics. Serie B</jtitle><stitle>Chin. Ann. Math. Ser. B</stitle><date>2019</date><risdate>2019</risdate><volume>40</volume><issue>1</issue><spage>55</spage><epage>64</epage><pages>55-64</pages><issn>0252-9599</issn><eissn>1860-6261</eissn><abstract>Given a triangle functor
F
:
A
→
B
, the authors introduce the half image hIm
F
, which is an additive category closely related to
F
. If
F
is full or faithful, then hIm
F
admits a natural triangulated structure. However, in general, one can not expect that hIm
F
has a natural triangulated structure. The aim of this paper is to prove that hIm
F
admits a natural triangulated structure if and only if
F
satisfies the condition (SM). If this is the case, hIm
F
is triangle-equivalent to the Verdier quotient
A
/Ker
F
.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s11401-018-0117-1</doi><tpages>10</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0252-9599 |
| ispartof | Chinese annals of mathematics. Serie B, 2019, Vol.40 (1), p.55-64 |
| issn | 0252-9599 1860-6261 |
| language | eng |
| recordid | cdi_wanfang_journals_sxnk_e201901003 |
| source | Springer Online Journals Complete; Alma/SFX Local Collection |
| subjects | Applications of Mathematics Kerf Mathematics Mathematics and Statistics |
| title | Triangulated Structures Induced by Triangle Functors |
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