Model structure on the category of small topological categories

Amrani, I.: Categories simpliciales enrichies et K-Theorie de Waldhausen. PhD thesis (2010)

Berger, C., Moerdijk, I.: Axiomatic homotopy theory for operads. Comment. Math. Helvetici 78(4) (2003)

Berger, C., Moerdijk, I.: On the homotopy theory of enriched categories (preprint, arXiv:1201.2134, 2012)

Bergner, J.E.: A model category structure on the category of simplicial categories. Trans. Am. Math. Soc. 359(5), 2043 (2007)

Drinfeld, V.: Dg quotients of dg categories. J. Algebra 272(2), 643–691 (2004)

Fritsch, R., Piccinini, R.: Cellular Structures in Topology, vol. 19. Cambridge University Press, Cambridge (1990)

Tabuada, G.: A new quillen model for the Morita homotopy theory of dg categories. (arxiv, preprint math/0701205, 2007)