  In the last year of his life, Bob Thomason reworked the notion of a model
category, used to adapt homotopy theory to algebra, and used homotopy ends to
affirmatively solve a problem raised by Grothendieck: find a notion of model
structure which is inherited by functor categories. In this paper we explain
and prove Thomason's results, based on his private notebooks.
  The first half presents Thomason's ideas about homotopy ends and its
generalizations. This material may be of independent interest. Then we define
Thomason model categories and give some examples. The usual proof shows that
the homotopy category exists.
  In the last two sections we prove the main theorem: functor categories
inherit a Thomason model structure, at least when the original category is
enriched over simplicial sets and fibrations are preserved by limits.
