# Fibration structure for Gromov h-principle

@inproceedings{Yamazaki2021FibrationSF, title={Fibration structure for Gromov h-principle}, author={Koji Yamazaki}, year={2021} }

The h-principle is a powerful tool for obtaining solutions to partial differential inequalities and partial differential equations. Gromov discovered the h-principle for the general partial differential relations to generalize the results of Hirsch and Smale. In his book, Gromov generalizes his theorem and discusses the sheaf theoretic h-principle, in which an object called a flexible sheaf plays an important role. We show that a flexible sheaf can be interpreted as a fibrant object with…

## One Citation

### Condensed Sets on Compact Hausdorff Spaces

- Mathematics
- 2022

A condensed set is a sheaf on the site of Stone spaces and continuous maps. We prove that condensed sets are equivalent to sheaves on the site of compact Hausdorﬀ spaces and continuous maps. As an…

## References

SHOWING 1-10 OF 44 REFERENCES

### Holonomic approximation and Gromov's h-principle

- Mathematics
- 2001

In 1969 M. Gromov in his PhD thesis greatly generalized Smale-Hirsch-Phillips immersion-submersion theory by proving what is now called the h-principle for invariant open differential relations over…

### The HELP-Lemma and its converse in Quillen model categories

- Mathematics
- 2010

We show that a map between fibrant objects in a closed model category is a weak equivalence if and only if it has the right homotopy extension lifting property with respect to all cofibrations. The…

### Cofibrations in Homotopy Theory

- Mathematics
- 2006

We define Anderson-Brown-Cisinski (ABC) cofibration categories, and construct homotopy colimits of diagrams of objects in ABC cofibration categories. Homotopy colimits for Quillen model categories…

### ∞-Categories for the Working Mathematician

- Mathematics
- 2018

homotopy theory C.1. Lifting properties, weak factorization systems, and Leibniz closure C.1.1. Lemma. Any class of maps characterized by a right lifting property is closed under composition,…

### Sheaves in geometry and logic: a first introduction to topos theory

- Mathematics
- 1992

This text presents topos theory as it has developed from the study of sheaves. Sheaves arose in geometry as coefficients for cohomology and as descriptions of the functions appropriate to various…

### Partial Differential Relations

- Mathematics
- 1986

1. A Survey of Basic Problems and Results.- 2. Methods to Prove the h-Principle.- 3. Isometric C?-Immersions.- References.- Author Index.

### Simplicial Homotopy Theory

- MathematicsModern Birkhäuser Classics
- 2009

Simplicial sets, model categories, and cosimplicial spaces: applications for homotopy coherence, results and constructions, and more.

### A classification of immersions of the two-sphere

- Mathematics
- 1959

An immersion of one C' differentiable manifold in another is a regular map (a C' map whose Jacobian is of maximum rank) of the first into the second. A homotopy of an immersion is called regular if…