Covers, envelopes, and cotorsion theories in locally presentable abelian categories and contramodule categories

摘要

We prove general results about completeness of cotorsion theories andexistence of covers and envelopes in locally presentable abelian categories,extending the well-established theory for module categories and Grothendieckcategories. These results are then applied to the categories of contramodulesover topological rings, which provide examples and counterexamples.