Homological Algebra for Banach Modules?
نویسندگان
چکیده
Injectivity is an important concept in algebra, homotopy theory and elsewhere. We study the ‘injectivity consequence’ of morphisms of a category: a morphism h is a consequence of a set H of morphisms if every object injective w.r.t. all members of H is also injective w.r.t. h. We formulate a very simple logic which is always sound, i.e., whenever a proof of h from assumptions in H exists, then h is a consequence of H . In a wide range of categories (including e.g. all locally presentable categories and the category of topological spaces) we prove the completeness: every consequence can be proved. This is a joint work with Michel Hébert and Lurdes Sousa.
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