Jardine, J. F. Modelling homotopy coherence. (English) Zbl 0785.18003 Seely, R. A. G. (ed.), Category theory 1991. Proceedings of an international summer category theory meeting, held in Montréal, Québec, Canada, June 23-30, 1991. Providence, RI: American Mathematical Society. CMS Conf. Proc. 13, 267-283 (1992). The author introduces a non-standard notion of homotopy coherent diagram on a category \(C\), which copes well with lax functors. He proves a realisation theorem (Proposition 5, based on Theorem 4): a homotopy coherent diagram gives a genuine functor on \(C\) with good properties. He also proves a version of Quillen’s Theorem B.For the entire collection see [Zbl 0771.00047]. Reviewer: R.J.Steiner (Glasgow) MSC: 18G30 Simplicial sets; simplicial objects in a category (MSC2010) 55P65 Homotopy functors in algebraic topology 55U35 Abstract and axiomatic homotopy theory in algebraic topology Keywords:homotopy coherence; lax functors; Quillen’s Theorem B PDFBibTeX XMLCite \textit{J. F. Jardine}, CMS Conf. Proc. 13, 267--283 (1992; Zbl 0785.18003)