Homotopy equivalence of normalized and unnormalized complexes, revisited
We consider the unnormalized and normalized complexes of a simplicial or a cosimplicial object coming from the Dold-Kan correspondence for an idempotent complete additive category (kernels and cokernels are not required). The normalized complex is defined as the image of certain idempotent in the un...
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| Дата: | 2022 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2022
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1879 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-18792022-03-28T05:34:02Z Homotopy equivalence of normalized and unnormalized complexes, revisited Lyubashenko, V. Matsui, A. idempotent, simplicial object; homotopy in chain complexes, Dold--Kan correspondence 18G31, 18N50 We consider the unnormalized and normalized complexes of a simplicial or a cosimplicial object coming from the Dold-Kan correspondence for an idempotent complete additive category (kernels and cokernels are not required). The normalized complex is defined as the image of certain idempotent in the unnormalized complex. We prove that this idempotent is homotopic to identity via homotopy which is expressed via faces and degeneracies. Hence, the normalized and unnormalized complex are homotopy isomorphic to each other. We provide explicit formulae for the homotopy. Lugansk National Taras Shevchenko University 2022-03-28 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1879 10.12958/adm1879 Algebra and Discrete Mathematics; Vol 32, No 2 (2021) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1879/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1879/925 Copyright (c) 2022 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
idempotent simplicial object; homotopy in chain complexes Dold--Kan correspondence 18G31 18N50 |
| spellingShingle |
idempotent simplicial object; homotopy in chain complexes Dold--Kan correspondence 18G31 18N50 Lyubashenko, V. Matsui, A. Homotopy equivalence of normalized and unnormalized complexes, revisited |
| topic_facet |
idempotent simplicial object; homotopy in chain complexes Dold--Kan correspondence 18G31 18N50 |
| format |
Article |
| author |
Lyubashenko, V. Matsui, A. |
| author_facet |
Lyubashenko, V. Matsui, A. |
| author_sort |
Lyubashenko, V. |
| title |
Homotopy equivalence of normalized and unnormalized complexes, revisited |
| title_short |
Homotopy equivalence of normalized and unnormalized complexes, revisited |
| title_full |
Homotopy equivalence of normalized and unnormalized complexes, revisited |
| title_fullStr |
Homotopy equivalence of normalized and unnormalized complexes, revisited |
| title_full_unstemmed |
Homotopy equivalence of normalized and unnormalized complexes, revisited |
| title_sort |
homotopy equivalence of normalized and unnormalized complexes, revisited |
| description |
We consider the unnormalized and normalized complexes of a simplicial or a cosimplicial object coming from the Dold-Kan correspondence for an idempotent complete additive category (kernels and cokernels are not required). The normalized complex is defined as the image of certain idempotent in the unnormalized complex. We prove that this idempotent is homotopic to identity via homotopy which is expressed via faces and degeneracies. Hence, the normalized and unnormalized complex are homotopy isomorphic to each other. We provide explicit formulae for the homotopy. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2022 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1879 |
| work_keys_str_mv |
AT lyubashenkov homotopyequivalenceofnormalizedandunnormalizedcomplexesrevisited AT matsuia homotopyequivalenceofnormalizedandunnormalizedcomplexesrevisited |
| first_indexed |
2024-04-12T06:26:31Z |
| last_indexed |
2024-04-12T06:26:31Z |
| _version_ |
1796109218342764544 |