Christ, Merlin and Dyckerhoff, Tobias and Walde, Tashi (2025) Lax additivity. DOCUMENTA MATHEMATICA. ISSN 1431-0635, 1431-0643
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We introduce notions of lax semiadditive and lax additive (infinity,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 (infinity,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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | additive; lax limit; 2-category; chain complex; categorification; homological algebra |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 06 May 2026 09:09 |
| Last Modified: | 06 May 2026 09:09 |
| URI: | https://pred.uni-regensburg.de/id/eprint/66969 |
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