HOMOLOGICAL ALGEBRA: The Interplay of Homology with Distributive Lattices and Orthodox Semigroups - Tapa dura

Acerca del autor

Charlotte y Peter Fiell son dos autoridades en historia, teoría y crítica del diseño y han escrito más de sesenta libros sobre la materia, muchos de los cuales se han convertido en éxitos de ventas. También han impartido conferencias y cursos como profesores invitados, han comisariado exposiciones y asesorado a fabricantes, museos, salas de subastas y grandes coleccionistas privados de todo el mundo. Los Fiell han escrito numerosos libros para TASCHEN, entre los que se incluyen 1000 Chairs, Diseño del siglo XX, El diseño industrial de la A a la Z, Scandinavian Design y Diseño del siglo XXI.

De la contraportada

In this book we want to explore aspects of coherence in homological algebra, that already appear in the classical situation of abelian groups or abelian categories.

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. A parallel role is played by semigroups of endorelations.

These links rest on the fact that many such systems, but not all of them, live in distributive sublattices of the modular lattices of subobjects of the system.

The property of distributivity allows one to work with induced morphisms in an automatically consistent way, as we prove in a 'Coherence Theorem for homological algebra'. (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.)

The same property of distributivity also permits representations of homological structures by means of sets and lattices of subsets, yielding a precise foundation for the heuristic tool of Zeeman diagrams as universal models of spectral sequences.

We thus establish an effective method of working with spectral sequences, called 'crossword chasing', that can often replace the usual complicated algebraic tools and be of much help to readers that want to apply spectral sequences in any field.