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In this paper we construct a monoidal model structure on the category of pointed curved coalgebras\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathsf{ptdCoa}^{*}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    over a field\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathbf{k}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    and show that the Quillen equivalence relating it to\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathsf{dgCat}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    is monoidal. We also show that\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathsf{dgCat}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    is a\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathsf{ptdCoa}^{*}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -enriched model category. As a consequence, the homotopy category of\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathsf{dgCat}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    is closed monoidal and is equivalent as a closed monoidal category to the homotopy category of\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathsf{ptdCoa}^{*}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . In particular, this gives a conceptual construction of a derived internal hom in\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathsf{dgCat}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    which we establish over a general PID. This proves Kontsevich\u2019s characterization of the internal hom in terms of\n                    <jats:inline-formula>\n                      <jats:tex-math>A_{\\infty}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -functors. As an application we obtain a new description of simplicial mapping spaces in\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathsf{dgCat}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    (over a field) and a calculation of their homotopy groups in terms of Hochschild cohomology groups, reproducing a well-known results of To\u00ebn. Comparing our approach to To\u00ebn\u2019s, we also obtain a description of the core of Lurie\u2019s dg nerve in terms of the ordinary nerve of a discrete category.\n                  <\/jats:p>","DOI":"10.4171\/dm\/1002","type":"journal-article","created":{"date-parts":[[2025,6,16]],"date-time":"2025-06-16T07:45:36Z","timestamp":1750059936000},"page":"755-786","source":"Crossref","is-referenced-by-count":0,"title":["Enriched Koszul duality for dg categories"],"prefix":"10.4171","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-9589-539X","authenticated-orcid":false,"given":"Julian","family":"Holstein","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00g30e956","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Hamburg, Hamburg, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9938-7174","authenticated-orcid":false,"given":"Andrey","family":"Lazarev","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04f2nsd36","id-type":"ROR","asserted-by":"publisher"}],"name":"Lancaster University, Lancaster, UK"}]}],"member":"2673","container-title":["Documenta Mathematica"],"deposited":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T13:32:37Z","timestamp":1762867957000},"score":16.750572,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/dm\/1002"}},"issued":{"date-parts":[[2025,6,16]]},"references-count":0,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.4171\/dm\/1002","ISSN":["1431-0635","1431-0643"],"issn-type":[{"type":"print","value":"1431-0635"},{"type":"electronic","value":"1431-0643"}],"published":{"date-parts":[[2025,6,16]]}},{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:51:37Z","timestamp":1760122297866},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2013,10,19]],"date-time":"2013-10-19T00:00:00Z","timestamp":1382140800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sel. 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Our results reveal that chronic A. yasumatsui infestations, combined with other invasive herbivore threats, have damaged the host C. micronesica population through a sustained reduction in ovule production and the percent seed set for each megastrobilus, thereby impairing regeneration. This plant response to the biotic threats is distinct from the ongoing mortality of mature trees and emerging seedlings. 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(2004). Guam\u2019s Forest Resources, 2002. Resource Bulletin PNW-RB-243.","DOI":"10.2737\/PNW-RB-243"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1017\/S0376892917000297","article-title":"Invasive alien species on islands: Impacts, distribution, interactions and management","volume":"44","author":"Russell","year":"2017","journal-title":"Environ. Conserv."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1146\/annurev-environ-101718-033245","article-title":"Island biodiversity in the Anthropocene","volume":"44","author":"Russell","year":"2019","journal-title":"Annu. Rev. Environ. Resourc."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"13391","DOI":"10.1038\/s41598-022-14982-5","article-title":"The global contribution of invasive vertebrate eradication as a key island restoration tool","volume":"12","author":"Spatz","year":"2022","journal-title":"Sci. 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