HOMOLOGICAL ALGEBRA

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Coherence in homological algebra is examined through the lens of abelian groups and categories, highlighting the significance of lattices of subobjects and semigroups of endorelations. The book presents a 'Coherence Theorem' that emphasizes the importance of distributivity in ensuring consistency within homological systems, contrasting it with the potential inconsistencies in non-distributive structures like bifiltered chain complexes. Additionally, it introduces 'crossword chasing' as a simplified method for working with spectral sequences, offering a practical alternative to traditional algebraic approaches.