Ranges of functors in algebra

Friedrich Wehrung (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

The problem of determining the range of a given functor arises in various parts of mathematics. We present a sample of such problems, with focus on various functors, arising in the contexts of nonstable K_0-theory of rings, congruence lattices of universal algebras, spectral spaces of ring-like objects. We also sketch some of the ideas involved in the solutions of those problems.

Mots clés: Category; functor; diagram; condensate; spectrum; sober space; spectral space; Stone duality; congruence; lattice; distributive; Murray - von~Neumann equivalence; nonstable K-theory

Domaines: Mathématiques générales [math.GM]

Friedrich Wehrung. Ranges of functors in algebra. The Mathematics Student, 2018, 87 (1-2), pp.67--81. ⟨hal-01856245⟩