HOMOLOGICAL ALGEBRA

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The study focuses on 'semiexact' and 'homological' categories, aiming to expand homological concepts into non-abelian contexts, where advanced tools like satellites and spectral sequences remain applicable. This work serves as a sequel to a prior book on homological algebra but can be understood independently. It introduces semiexact categories equipped with null morphisms, and homological categories that facilitate the construction of subquotients and induced morphisms. The framework encompasses traditional domains of homology and homotopy theories, including pairs of topological spaces and their actions on pointed sets.