### Representations of Spaces

, 2008

"... We explain how the notion of homotopy colimits gives rise to that of mapping spaces, even in categories which are not simplicial. We apply the technique of model approximations and use elementary properties of the category of spaces ..."

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We explain how the notion of homotopy colimits gives rise to that of mapping spaces, even in categories which are not simplicial. We apply the technique of model approximations and use elementary properties of the category of spaces

### DOI: 10.1007/s00222-007-0061-2 Triangulated categories without models

, 2007

"... Abstract. We exhibit examples of triangulated categories which are neither ..."

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Abstract. We exhibit examples of triangulated categories which are neither

### DOI: 10.1016/j.top.2003.10.008 A remark on K-theory and S-categories

, 2013

"... It is now well known that the K-theory of a Waldhausen category depends on more than just its (triangulated) homotopy category (see [20]). The purpose of this note is to show that the K-theory spectrum of a (good) Waldhausen category is completely determined by its Dwyer-Kan simplicial localization, ..."

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It is now well known that the K-theory of a Waldhausen category depends on more than just its (triangulated) homotopy category (see [20]). The purpose of this note is to show that the K-theory spectrum of a (good) Waldhausen category is completely determined by its Dwyer-Kan simplicial localization, without any additional structure. As the simplicial localization is a refined version of the homotopy category which also determines the triangulated structure, our result is a possible answer to the general question: “To which extent K-theory is not an invariant of triangulated derived categories?”

### Homology, Homotopy and Applications, vol. 10(3), 2008, pp.193–221 DIAGRAMS INDEXED BY GROTHENDIECK CONSTRUCTIONS

"... Let I be a small indexing category, G: I op → Cat be a functor and BG ∈ Cat denote the Grothendieck construction on G. ..."

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Let I be a small indexing category, G: I op → Cat be a functor and BG ∈ Cat denote the Grothendieck construction on G.

### ASPHERICITY STRUCTURES, SMOOTH FUNCTORS, AND

"... This paper was translated from French by Jonathan Chiche. Abstract. The aim of this paper is to generalize Grothendieck’s theory of smooth functors in order to include within this framework the theory of fibered categories. We obtain in particular a new characterization of fibered categories. ..."

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This paper was translated from French by Jonathan Chiche. Abstract. The aim of this paper is to generalize Grothendieck’s theory of smooth functors in order to include within this framework the theory of fibered categories. We obtain in particular a new characterization of fibered categories.

### Contents

, 2004

"... Abstract. A functor is constructed from the category of globular CW-complexes to that of flows. It allows to compare the S-homotopy equivalences (resp. the T-homotopy equivalences) of globular complexes with the S-homotopy equivalences (resp. the T-homotopy equivalences) of flows. Moreover, one prov ..."

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Abstract. A functor is constructed from the category of globular CW-complexes to that of flows. It allows to compare the S-homotopy equivalences (resp. the T-homotopy equivalences) of globular complexes with the S-homotopy equivalences (resp. the T-homotopy equivalences) of flows. Moreover, one proves that this functor induces an equivalence of categories from the localization of the category of globular CW-complexes with respect to S-homotopy equivalences to the localization of the category of flows with respect to weak