Further, it is shown that effective Kan fibrations are local, or completely determined by their fibres above representables, and the maps which can be equipped with the structure of an effective Kan fibration are precisely the ordinary Kan fibrations.
- 1. Introduction. - Part I -Π Types from Moore Paths. - 2. Preliminaries. - 3. An Algebraic Weak Factorisation System from a Dominance. - 4. An Algebraic Weak Factorisation System from a Moore Structure. - 5. The Frobenius Construction. - 6. Mould Squares and Effective Fibrations. - 7. Π-Types. - Part II Simplicial Sets. - 8. Effective Trivial Kan Fibrations in Simplicial Sets. - 9. Simplicial Sets as a Symmetric Moore Category. - 10. Hyperdeformation Retracts in Simplicial Sets. - 11. Mould Squares in Simplicial Sets. - 12. Horn Squares. - 13. Conclusion.