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For the class of fibrewise opfibrations in<jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathsf {Fib}}(B)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>Fib<\/mml:mi><mml:mo>(<\/mml:mo><mml:mi>B<\/mml:mi><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>, the construction of the latter two simplify to a single coidentifier (respectively coinverter) followed by an internal discrete opfibration (resp. fibrewise opfibration in groupoids). We show how these results follow from their analogues in<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathsf {Cat}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>Cat<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>, providing suitable conditions on a 2-category<jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathcal {C}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>C<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>, that allow the transfer of the construction of coinverters and coidentifiers from<jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathcal {C}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>C<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>\u00a0to<jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathsf {Fib}}_{{\\mathcal {C}}}(B)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:msub><mml:mi>Fib<\/mml:mi><mml:mi>C<\/mml:mi><\/mml:msub><mml:mrow><mml:mo>(<\/mml:mo><mml:mi>B<\/mml:mi><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1007\/s10485-020-09615-9","type":"journal-article","created":{"date-parts":[[2020,11,4]],"date-time":"2020-11-04T17:02:44Z","timestamp":1604509364000},"page":"249-265","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Discrete and Conservative Factorizations in Fib(B)"],"prefix":"10.1007","volume":"29","author":[{"given":"Alan S.","family":"Cigoli","sequence":"first","affiliation":[]},{"given":"Sandra","family":"Mantovani","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1839-3626","authenticated-orcid":false,"given":"Giuseppe","family":"Metere","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,11,4]]},"reference":[{"key":"9615_CR1","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.jalgebra.2016.03.015","volume":"458","author":"AS Cigoli","year":"2016","unstructured":"Cigoli, A.S., Metere, G.: Extension theory and the calculus of butterflies. 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