Coley, Ian

The theory of half derivators

Doc. Math. 27, 655-698 (2022)
DOI: 10.25537/dm.2022v27.655-698
Communicated by Mike Hill


We review the theory of derivators from the ground up, defining new classes of derivators which were originally motivated by derivator K-theory. We prove that many old arguments that relied on homotopical bicompleteness hold also for one-sided \textit{half derivators} on arbitrary diagram categories. We end by defining the maximal domain for a K-theory of derivators generalising Waldhausen K-theory.

Mathematics Subject Classification

18N40, 55U35


derivators, abstract homotopy theory, parametrized category, fibred category


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Coley, Ian
Department of Mathematics, Rutgers University, Hill Center for the Mathematical Sciences, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA