On the Smoothness of Functors

TL;DR

This paper proposes a new notion of smoothness for functors, drawing from geometric and algebraic properties, to better understand their behavior in mathematical contexts.

Contribution

It introduces a novel smoothness concept for functors inspired by geometric and algebraic principles, filling a gap in the theoretical framework.

Findings

Defines a new smoothness criterion for functors

Establishes properties expected of smooth functors

Provides conditions linking geometry and algebraic smoothness

Abstract

In this paper we try to introduce a good smoothness notion for a functor. We consider properties and conditions from geometry and algebraic geometry which we expect a smooth functor should to have.