# A generalization of Grothendieck's Extension Panach\'ees

## TL;DR

This paper generalizes the classical extension problem for exact sequences, providing a comprehensive criterion for existence and uniqueness of solutions, thereby extending foundational work in algebraic geometry.

## Contribution

It introduces a broad generalization of the extension problem and establishes necessary and sufficient conditions for solutions to exist and be unique.

## Key findings

- Derived a criterion for the existence of solutions
- Established conditions for the uniqueness of solutions
- Extended classical extension theory in algebraic geometry

## Abstract

We formulate a generalization of the extension problem for exact sequences which was considered in [SGA VII] and give a necessary and sufficient criterion for the solution to exist. We also remark on the criterion under which such a solution is unique, if it exists.