Lax Additivity
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911269145018368 |
|---|---|
| author | Christ, Merlin Dyckerhoff, Tobias Walde, Tashi |
| author_facet | Christ, Merlin Dyckerhoff, Tobias Walde, Tashi |
| contents | We introduce notions of lax semiadditive and lax additive $(\infty,2)$-categories, categorifying the classical notions of semiadditive and additive 1-categories. To establish a well-behaved axiomatic framework, we develop a calculus of lax matrices and use it to prove that in locally cocomplete $(\infty,2)$-categories lax limits and lax colimits agree and are absolute. In the lax additive setting, we categorify fundamental constructions from homological algebra such as mapping complexes and mapping cones and establish their basic properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12251 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lax Additivity Christ, Merlin Dyckerhoff, Tobias Walde, Tashi Category Theory Algebraic Topology 18N65, 18E05, 18N25, 18G35 We introduce notions of lax semiadditive and lax additive $(\infty,2)$-categories, categorifying the classical notions of semiadditive and additive 1-categories. To establish a well-behaved axiomatic framework, we develop a calculus of lax matrices and use it to prove that in locally cocomplete $(\infty,2)$-categories lax limits and lax colimits agree and are absolute. In the lax additive setting, we categorify fundamental constructions from homological algebra such as mapping complexes and mapping cones and establish their basic properties. |
| title | Lax Additivity |
| topic | Category Theory Algebraic Topology 18N65, 18E05, 18N25, 18G35 |
| url | https://arxiv.org/abs/2402.12251 |