Universal property of the category of bounded chain complexes on exact categories, by Satoshi Mochizuki

The purpose of this note is to establish universal property of the category of bounded chain complexes on an exact category. More accurately saying that we define the notion of (bi)complicial categories which are exact categories with the extra structures and it is a simplification of the concept about Thomason-Trobaugh or Schlichting complicial exact categories. For example, the category of bounded chain complexes on an exact category has the natural (bi)complicial structure. The first main theorem is that associating an exact category E with the category of bounded chain complexes Ch_b(E) is the universal bicomplification. The theorem is considered as a variant of Bökstedt-Neeman totalization functor construction on a triangulated category. As usual completion functors are idempotent, the bicomplification is also idempotent in some sense. More precise statement is described as a derived analogue of Gillet-Waldhausen theorem.


Satoshi Mochizuki <mochi81@hotmail.com>