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Algebraic K Theory

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3 domain-specific abstractions whose origin domain is Algebraic K Theory.

  • Milnor K-theory — The graded ring generated by nonzero field elements modulo Steinberg relations, linking symbols in algebraic K-theory with Galois cohomology.
  • Steinberg group (K-theory) — Present the universal central extension of the stable elementary linear group of a ring by generators x_ij(a) and Steinberg commutator relations.
  • Waldhausen category — A category equipped with designated cofibrations and weak equivalences satisfying gluing axioms so its algebraic K-theory spectrum can be constructed by the S-construction.