We develop the K-theory of sets with an action of a pointed monoid (or monoid scheme), analogous to the K-theory of modules over a ring (or scheme). In order to form localization sequences, we construct the quotient category of a nice regular category by a Serre subcategory.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Algebraic K-theory
- Monoid sets
- Pointed monoids