A devissage theorem for modular exact categories with weak equivalences, by Satoshi Mochizuki

In this note, we will introduce a concept of modularity of exact categories due to Masana Harada. The naming is coming from the classical modular lattices theory. We will also state and prove so-called homotopy Grayson-Staffeldt-Jordan-Holder theorem which is implicitly appeared in [Gra87] and [Sta89]. The theorem says contractibility of a simplicial set associated to a certain upper semi-lattice. Combining these two ideas and utilizing Waldhausen's technique in [Wal85], we will get a devissage theorem for modular exact categories with weak equivalences which is a generalization of original Quillen's one in [Qui73].

[January 28 version replaced February 1. An "idempotent completeness assumption" has been removed.]


Satoshi Mochizuki <mochi81@hotmail.com>