Homology of higher categories
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911653585485824 |
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| author | Heine, Hadrian |
| author_facet | Heine, Hadrian |
| contents | Homology is characterized by the Eilenberg-Steenrod axioms. We define homology of higher categories via a categorical analogue of the Eilenberg-Steenrod axioms. We prove a categorical Dold-Kan correspondence, providing a combinatorial presentation of categorical homology in which the Street nerve plays the role of the singular complex. This implies a categorical Dold-Thom theorem that endows categorical homology with a multiplicative structure and leads to computations of categorical homology of the globes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22640 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homology of higher categories Heine, Hadrian Algebraic Topology Category Theory K-Theory and Homology Homology is characterized by the Eilenberg-Steenrod axioms. We define homology of higher categories via a categorical analogue of the Eilenberg-Steenrod axioms. We prove a categorical Dold-Kan correspondence, providing a combinatorial presentation of categorical homology in which the Street nerve plays the role of the singular complex. This implies a categorical Dold-Thom theorem that endows categorical homology with a multiplicative structure and leads to computations of categorical homology of the globes. |
| title | Homology of higher categories |
| topic | Algebraic Topology Category Theory K-Theory and Homology |
| url | https://arxiv.org/abs/2505.22640 |