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In this model structure every object is fibrant and the cofibrant objects have cofibrant morphisms. As a consequence we prove that the semi-free\n \n \n $$\\text{ A}_{\\infty }$$<\/jats:tex-math>\n \n \n \n \n A<\/mml:mtext>\n \u221e<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n -categories (resp. resolutions) are cofibrant objects (resp. resolution) in this model structure.\n <\/jats:p>","DOI":"10.1007\/s10485-026-09870-2","type":"journal-article","created":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T07:40:25Z","timestamp":1777880425000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Model Structure on the Category of $$\\text{ A}_{\\infty }$$-Categories with Strict Morphisms"],"prefix":"10.1007","volume":"34","author":[{"given":"Mattia","family":"Ornaghi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,4]]},"reference":[{"key":"9870_CR1","unstructured":"Avramov, L., Foxby, H.B., Halperin, S.: Differential graded homological algebra. 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