Homological Algebra: The Interplay Of Homology With Distributive Lattices And Orthodox Semigroups by Marco Grandis (Hardcover, 2012)

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Lattices of subobjects are shown to play an important role in the study of homological systems, from simple chain complexes to all the structures that give rise to spectral sequences. (On the contrary, a ‘non-distributive’ homological structure like the bifiltered chain complex can easily lead to inconsistency, if one explores the interaction of its two spectral sequences farther than it is normally done.).