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We show that any exact structure on a small idempotent-complete additive category extends uniquely to a locally coherent exact structure on the category of ind-objects; in particular, any finitely accessible category has the unique maximal and the unique minimal locally coherent exact category structures. All locally coherent exact categories are of Grothendieck type in the sense of \u0160t\u2019ov\u00ed\u010dek. We also discuss the canonical embedding of a small exact category into the abelian category of additive sheaves in connection with the locally coherent exact structure on the ind-objects, and deduce two periodicity theorems as applications.<\/jats:p>","DOI":"10.1007\/s10485-024-09780-1","type":"journal-article","created":{"date-parts":[[2024,7,26]],"date-time":"2024-07-26T21:02:01Z","timestamp":1722027721000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Locally Coherent Exact Categories"],"prefix":"10.1007","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8836-3911","authenticated-orcid":false,"given":"Leonid","family":"Positselski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,26]]},"reference":[{"key":"9780_CR1","unstructured":"Ad\u00e1mek, J., Rosick\u00fd, J.: Locally presentable and accessible categories. 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