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Struct"],"published-print":{"date-parts":[[2025,2]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Let <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$${{\\mathcal {O}}}\\rightarrow {\\text {BM}}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>O<\/mml:mi>\n                    <mml:mo>\u2192<\/mml:mo>\n                    <mml:mtext>BM<\/mml:mtext>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> be a <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$${\\text {BM}}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mtext>BM<\/mml:mtext>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-operad that exhibits an <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\infty $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u221e<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-category <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$${{\\mathcal {D}}}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>D<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> as weakly bitensored over non-symmetric <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\infty $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u221e<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-operads <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$${{\\mathcal {V}}}\\rightarrow \\text {Ass }, {{\\mathcal {W}}}\\rightarrow \\text {Ass }$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>V<\/mml:mi>\n                    <mml:mo>\u2192<\/mml:mo>\n                    <mml:mtext>Ass<\/mml:mtext>\n                    <mml:mspace\/>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mi>W<\/mml:mi>\n                    <mml:mo>\u2192<\/mml:mo>\n                    <mml:mtext>Ass<\/mml:mtext>\n                    <mml:mspace\/>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> and <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$${{\\mathcal {C}}}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>C<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> a <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$${{\\mathcal {V}}}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>V<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-enriched <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\infty $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u221e<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-precategory. We construct an equivalence <jats:disp-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\begin{aligned} \\text {Fun}_{\\text {Hin}}^{{\\mathcal {V}}}({{\\mathcal {C}}},{{\\mathcal {D}}}) \\simeq \\text {Fun}^{{\\mathcal {V}}}({{\\mathcal {C}}},{{\\mathcal {D}}}) \\end{aligned}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mtable>\n                      <mml:mtr>\n                        <mml:mtd>\n                          <mml:mrow>\n                            <mml:msubsup>\n                              <mml:mtext>Fun<\/mml:mtext>\n                              <mml:mrow>\n                                <mml:mtext>Hin<\/mml:mtext>\n                              <\/mml:mrow>\n                              <mml:mi>V<\/mml:mi>\n                            <\/mml:msubsup>\n                            <mml:mrow>\n                              <mml:mo>(<\/mml:mo>\n                              <mml:mi>C<\/mml:mi>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:mi>D<\/mml:mi>\n                              <mml:mo>)<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mo>\u2243<\/mml:mo>\n                            <mml:msup>\n                              <mml:mtext>Fun<\/mml:mtext>\n                              <mml:mi>V<\/mml:mi>\n                            <\/mml:msup>\n                            <mml:mrow>\n                              <mml:mo>(<\/mml:mo>\n                              <mml:mi>C<\/mml:mi>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:mi>D<\/mml:mi>\n                              <mml:mo>)<\/mml:mo>\n                            <\/mml:mrow>\n                          <\/mml:mrow>\n                        <\/mml:mtd>\n                      <\/mml:mtr>\n                    <\/mml:mtable>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:disp-formula>of <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\infty $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u221e<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-categories weakly right tensored over <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$${{\\mathcal {W}}}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>W<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> between Hinich\u2019s construction of <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$${{\\mathcal {V}}}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>V<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-enriched functors of Hinich (Adv Math 367:107129, 2020) and our construction of <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$${{\\mathcal {V}}}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>V<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>-enriched functors of Heine (Adv Math 417:108941, 2023).\n<\/jats:p>","DOI":"10.1007\/s10485-024-09792-x","type":"journal-article","created":{"date-parts":[[2024,11,26]],"date-time":"2024-11-26T12:27:14Z","timestamp":1732624034000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Equivalence Between Two Models of $$\\infty $$-Categories of Enriched Presheaves"],"prefix":"10.1007","volume":"33","author":[{"given":"Hadrian","family":"Heine","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,11,26]]},"reference":[{"key":"9792_CR1","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1016\/j.aim.2015.02.007","volume":"279","author":"D Gepner","year":"2015","unstructured":"Gepner, D., Haugseng, R.: Enriched $$\\infty $$-categories via non-symmetric $$\\infty $$-operads. 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