## Abstract

If all objects of a simplicial combinatorial model category A are cofibrant, we construct the homotopy model structure on the category of small functors S A, where the fibrant objects are the levelwise fibrant homotopy functors, ie functors preserving weak equivalences. When A fails to have all objects cofibrant, we construct the bifibrant-projective model structure on S A and prove that it is an adequate substitute for the homotopy model structure. Next, we generalize a theorem of Dwyer and Kan, characterizing which functors f W A ! B induce a Quillen equivalence S A S B with the model structures above. We include an application to Goodwillie calculus, and we prove that the category of small linear functors from simplicial sets to simplicial sets is Quillen equivalent to the category of small linear functors from topological spaces to simplicial sets.

Original language | English |
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Pages (from-to) | 2185-2208 |

Number of pages | 24 |

Journal | Algebraic and Geometric Topology |

Volume | 24 |

Issue number | 4 |

DOIs | |

State | Published - 2024 |

### Bibliographical note

Publisher Copyright:© 2024 MSP

## Keywords

- bifibrant projective
- fibrant projective
- infinity categories
- model categories
- small functors

## ASJC Scopus subject areas

- Geometry and Topology