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To do this we provide another description of the completion of an approximable triangulated category under a properness assumption. We apply our results to proper schemes, proper connective DG-algebras and Azumaya algebras over proper schemes. We include an appendix by Raedschelders and Stevenson showing that proper connective DG-algebras admit finite dimensional models over any field.<\/jats:p>","DOI":"10.1007\/s10485-026-09856-0","type":"journal-article","created":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T12:30:54Z","timestamp":1774182654000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Approximable Triangulated Categories and Reflexive DG-categories"],"prefix":"10.1007","volume":"34","author":[{"given":"Isambard","family":"Goodbody","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,3,22]]},"reference":[{"issue":"780","key":"9856_CR1","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1515\/crelle-2021-0034","volume":"2021","author":"K Aoki","year":"2021","unstructured":"Aoki, K.: Quasiexcellence implies strong generation. 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