A dévissage-type theorem in algebraic
-theory is a statement that
identifies the
-theory of
a Waldhausen category
in terms of the
-theories
of a collection of Waldhausen subcategories of
when
a dévissage condition about the existence of appropriate finite filtrations is satisfied.
We distinguish between dévissage theorems of
single type and of
multiple type
depending on the number of Waldhausen subcategories and their properties. The
main representative examples of such theorems are Quillen’s original dévissage
theorem for abelian categories (single type) and Waldhausen’s theorem on spherical
objects for more general Waldhausen categories (multiple type). In this paper, we
study some general aspects of dévissage-type theorems and prove a general
dévissage theorem of single type and a general dévissage theorem of multiple
type.
