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starting page on (infinity,1)-equalizers with references
Jacob Lurie, section 4.4.3 of: Higher Topos Theory, Annals of Mathematics Studies 170, Princeton University Press 2009 (pup:8957, pdf)
Denis-Charles Cisinski, Bastiaan Cnossen, Kim Nguyen, Tashi Walde, section 5.6 of: Formalization of Higher Categories, work in progress (pdf)
that make it clear that they are talking about coequalizers in (infinity,1)-categories and not homotopy coequalizers in model categories
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moving material from coequalizer in simplicial type theory to this article
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