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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| Datum: | 2021 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2021
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| Schriftenreihe: | Algebra and Discrete Mathematics |
| Online Zugang: | 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 |
| Zitieren: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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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