10 citations · 15 across the 8 of their papers we have counts for
9 papers
Some Structures arising from the Farey Fractal
Shai Haran
This work explores new arithmetic and combinatorial structures arising from the interplay between Farey-type graphs, Fibonacci expansions, and operadic constructions. We introduce…
Non Additive Geometry
Shai Haran
The usual dictionary between geometry and commutative algebra is not appropriate for Arithmetic geometry because addition is a singular operation at the "Real prime". We replace Ri…
Non-Additive Geometry and Frobenius Correspondences
Shai Haran
The usual language of algebraic geometry is not appropriate for Arithmetical geometry: addition is singular at the real prime. We developed two languages that overcome this problem…
Homotopy and Arithmetic
Shai Haran
We define the concept of a bi-operad. We develop the homotopy theory of "Bital-Sets" and of infinite-bi-operads. We develop a geometry of generalized schemes based on the spectra o…
Meditations on the Farey Fractal
Shai Haran
We study the paths in the Farey graph going from (1,0) to (0,1) , or the finite subtrees of the Stern-Brocot tree . We show they form an operad and isolate the "coronas", which are…
Algebra over generalized rings
Shai Haran
For a commutative ring , we have the category of (bounded-below) chain complexes of -modules $Ch_{+}(A\mymod)$, a closed symmetric monoidal category with a compatible stable…
Geometry over F1
Shai Haran
We give (two) non additive languages for geometry via simple generalisations of commutative rings.
New foundations for geometry
Shai Haran
We shall describe a simple generalization of commutative rings. The category GR of such "rings", contains the ordinary commutative rings (fully faithfully), but also the "integers"…
Non-Additive Prolegomena (to any future Arithmetic that will be able to present itself as a Geometry)
Shai M. J. Haran
We give a language for geometry which makes curves and number fields look alike.