Chapter 1. Introduction ........................................ 1
Chapter 2. Review of some homotopical algebra .................. 9
Chapter 3. Review of the convergent topos ..................... 19
Chapter 4. Simplicial presheaves associated to isocrystals .... 29
Chapter 5. Simplicial presheaves associated to smooth
sheaves ............................................ 47
Chapter 6. The comparison theorem ............................. 63
Chapter 7. Proofs of 1.7-1.13 ................................. 73
Chapter 8. A base point free version .......................... 85
Chapter 9. Tangential base points ............................. 97
Chapter 10. A generalization .................................. 123
Appendix A. Exactification .................................... 125
Appendix B. Remarks on localization in model categories ....... 135
Appendix C. The coherator for algebraic stacks ................ 139
Appendix D.  cris(V)-admissible implies crystalline ............ 147
Bibliography .................................................. 155
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