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...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2021 |
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| Language: | English |
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Інститут прикладної математики і механіки НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188752 |
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| Cite this: | 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. |
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Lyubashenko, V. Matsui, A. 2023-03-14T17:07:32Z 2023-03-14T17:07:32Z 2021 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 https://nasplib.isofts.kiev.ua/handle/123456789/188752 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Homotopy equivalence of normalized and unnormalized complexes, revisited Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Homotopy equivalence of normalized and unnormalized complexes, revisited |
| spellingShingle |
Homotopy equivalence of normalized and unnormalized complexes, revisited Lyubashenko, V. Matsui, A. |
| 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 |
| author |
Lyubashenko, V. Matsui, A. |
| author_facet |
Lyubashenko, V. Matsui, A. |
| publishDate |
2021 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
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| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.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. |
| work_keys_str_mv |
AT lyubashenkov homotopyequivalenceofnormalizedandunnormalizedcomplexesrevisited AT matsuia homotopyequivalenceofnormalizedandunnormalizedcomplexesrevisited |
| first_indexed |
2025-12-01T10:17:05Z |
| last_indexed |
2025-12-01T10:17:05Z |
| _version_ |
1850859907101753344 |