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 DoldśKan 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...
Збережено в:
| Дата: | 2021 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2021
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/188752 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Homotopy equivalence of normalized and unnormalized complexes, revisited / V. Lyubashenko, A. Matsui // Algebra and Discrete Mathematics. — 2021. — Vol. 32, № 2. — С. 253-266. — Бібліогр.: 7 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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dspace |
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irk-123456789-1887522023-03-15T01:27:23Z Homotopy equivalence of normalized and unnormalized complexes, revisited Lyubashenko, V. Matsui, A. We consider the unnormalized and normalized complexes of a simplicial or a cosimplicial object coming from the DoldśKan 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. 2021 Article Homotopy equivalence of normalized and unnormalized complexes, revisited / V. Lyubashenko, A. Matsui // Algebra and Discrete Mathematics. — 2021. — Vol. 32, № 2. — С. 253-266. — Бібліогр.: 7 назв. — англ. 1726-3255 DOI:10.12958/adm1879 2020 MSC: 18G31, 18N50 http://dspace.nbuv.gov.ua/handle/123456789/188752 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We consider the unnormalized and normalized complexes of a simplicial or a cosimplicial object coming from the DoldśKan 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. |
| format |
Article |
| author |
Lyubashenko, V. Matsui, A. |
| spellingShingle |
Lyubashenko, V. Matsui, A. Homotopy equivalence of normalized and unnormalized complexes, revisited Algebra and Discrete Mathematics |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2021 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/188752 |
| citation_txt |
Homotopy equivalence of normalized and unnormalized complexes, revisited / V. Lyubashenko, A. Matsui // Algebra and Discrete Mathematics. — 2021. — Vol. 32, № 2. — С. 253-266. — Бібліогр.: 7 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT lyubashenkov homotopyequivalenceofnormalizedandunnormalizedcomplexesrevisited AT matsuia homotopyequivalenceofnormalizedandunnormalizedcomplexesrevisited |
| first_indexed |
2023-10-18T23:09:05Z |
| last_indexed |
2023-10-18T23:09:05Z |
| _version_ |
1796157379820126208 |