ACYCLIC MODELS

Acyclic models is a powerful technique in algebraic topology and homol ogical algebra in which facts about homology theories are verified by first verifying them on ''models'' (on which the homology theory is tr ivial) and then showing that there are enough models to present arbitr ary objects. One version of the theorem allows one to conclude that tw o chain complex functors are naturally homotopic and another that two such functors are object-wise homologous. Neither is entirely satisfac tory. The purpose of this paper is to provide a uniform account of the se two, fixing what is unsatisfactory and also finding intermediate fo rms of the theorem.