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We provide a concrete description of completions of bounded derived categories of hereditary finite dimensional algebras of finite representation type. In order to investigate completions of\u00a0bounded derived categories of algebras of finite global dimension, we define image and preimage metrics under a triangulated functor and use them to\u00a0induce a triangulated equivalence between two completions. Furthermore, for a given metric on a\u00a0triangulated category we construct a new, closely related good metric called the improvement and compare the respective completions.<\/jats:p>","DOI":"10.1007\/s10485-026-09857-z","type":"journal-article","created":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T07:34:25Z","timestamp":1777880065000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Metric Completions of Triangulated Categories from Finite Dimensional Algebras"],"prefix":"10.1007","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-0299-7021","authenticated-orcid":false,"given":"Cyril","family":"Matou\u0161ek","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,4]]},"reference":[{"key":"9857_CR1","doi-asserted-by":"crossref","unstructured":"Frank, W.: Anderson and Kent R. Fuller. 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