English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Let $k$ be a commutative Noetherian ring and $\underline{\mathscr{C}}$ be alocally finite $k$-linear category equipped with a self-embedding functor ofdegree 1. We show under a moderate condition that finitely generated torsionrepresentations of $\underline{\mathscr{C}}$ are super finitely presented (thatis, they have projective resolutions each term of which is finitely generated).In the situation that these self-embedding functors are genetic functors, wegive upper bounds for homological degrees of finitely generated torsionmodules. These results apply to quite a few categories recently appearing inrepresentation stability theory. In particular, when $k$ is a field ofcharacteristic 0, we obtain another upper bound for homological degrees offinitely generated $\mathrm{FI}$-modules.

Homological degrees of representations of categories with shift functors