# Sublinear extension of Grothendieck Algebraic K--theory (This paper is dedicated to the 80-th anniversary of Yuri I. Manin)

## TL;DR

This paper constructs a commutative diagram linking algebraic and analytical objects, extending Grothendieck K-theory to include both smooth and nonsmooth analysis through canonical embeddings.

## Contribution

It introduces a new diagram connecting algebraic and analytical structures, extending Grothendieck K-theory to encompass nonsmooth analysis objects.

## Key findings

- Established a diagram linking algebraic and analytical objects
- Extended Grothendieck K-theory to include nonsmooth analysis
- Unified linear and sublinear analysis frameworks

## Abstract

A commutative diagram that connects the basic objects of commutative algebra with the main objects of commutative analysis is constructed. Namely, with the help of five types of canonical embeddings we constructed a diagram between two sets of objects: Abelian semigroups -- Abelian regular (cancellative) semigroups -- Abelian groups, on the first hand, and convex cones -- regular convex cones -- linear spaces, on the other hand. Thus, some extension of the Grothendieck algebraic K--theory arises, that includes the basic objects not only of linear (smooth) analysis but of sublinear (nonsmooth) analysis also.