Publication details
Cofibrant generation of pure monomorphisms in presheaf categories
| Authors | |
|---|---|
| Year of publication | 2026 |
| Type | Article in Periodical |
| Magazine / Source | Advances in Mathematics |
| MU Faculty or unit | |
| Citation | |
| web | https://www.sciencedirect.com/science/article/pii/S000187082600232X |
| Doi | https://doi.org/10.1016/j.aim.2026.111010 |
| Keywords | Cofibrant generation; Presheaf category; Acts; Stable independence; Pure monomorphism |
| Attached files | |
| Description | We characterise when the pure monomorphisms in a presheaf category SetC are cofibrantly generated in terms of the category C. In particular, when C is a monoid S this characterises cofibrant generation of pure monomorphisms between sets with an S-action in terms of S: this happens if and only if for all a, b ? there is c ? S such that a = cb or ca = b. We give a model-theoretic proof: we prove that our characterisation is equivalent to having a stable independence relation, which in turn is equivalent to cofibrant generation. As a corollary, we show that pure monomorphisms in acts over the multiplicative monoid of natural numbers are not cofibrantly generated. |
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