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Let be a commutative Noetherian ring and let C be a locally finite -linear category equipped with a self-embedding functor of degree 1. We show under a moderate condition that finitely generated torsion representations of C are super finitely presented (that is, they have projective resolutions, each term of which is finitely generated). In the situation that these self-embedding functors are genetic functors, we give upper bounds for homological degrees of finitely generated torsion modules.doi:10.1090/tran/7041 fatcat:phvnmby2lja37ctgcmpxb4xzm4