Categorical homotopy theory

Categorical homotopy theory

Categorical Homotopy Theory

This paper is an exposition of the ideas and methods of Cisinksi, in the context of A-presheaves on a small Grothendieck site, where A is an arbitrary test category in the sense of Grothendieck. The homotopy theory for the category of simplicial presheaves and each of its localizations can be modelled by A-presheaves in the sense that there is a corresponding model structure for A-presheaves wi...

Homotopy Classification of Categorical Torsors

The long-known results of Schreier on group extensions are here raised to a categorical level by giving a factor set theory for torsors under a categorical group (G,⊗) over a small category B. We show a natural bijection between the set of equivalence classes of such torsors and [B(B),B(G,⊗)], the set of homotopy classes of continuous maps between the corresponding classifying spaces. These res...

Categorical aspects of equivariant homotopy

Homotopy Theory of Homotopy Algebras

The goal of this paper is to study the homotopy theory of homotopy algebras over a Koszul operad with their infinity morphisms. The method consists in endowing the category of coalgebras over the Koszul dual cooperad with a model category structure. CONTENTS Introduction 1 1. Recollections 2 2. Model category structure for coalgebras 5 3. Conclusion 14 Appendix A. A technical lemma 15 Reference...