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Abstract

Coherent functors ${{\cal S}}\to \mathop {\rm Ab}\nolimits $ from a compactly generated triangulated category into the category of abelian groups are studied. This is inspired by Auslander's classical analysis of coherent functors from a fixed abelian category into abelian groups. We characterize coherent functors and their filtered colimits in various ways. In addition, we investigate certain subcategories of ${{\cal S}}$ which arise from families of coherent functors.