# Derived Functor Cohomology Groups with Yoneda Product

## TL;DR

This paper explores the structure of derived categories in abelian categories and their applications in algebraic geometry, focusing on morphism calculations using Yoneda products and sheaf cohomology.

## Contribution

It provides a detailed exposition of derived category structures and introduces methods for computing morphisms via Yoneda products in algebraic geometry contexts.

## Key findings

- Computed morphisms in derived categories using Yoneda construction
- Applied cohomology calculations to projective geometry cases
- Enhanced understanding of derived functor cohomology groups

## Abstract

This work presents an exposition of both the internal structure of derived category of an abelian category D*(A) and its contribution in solving problems, particularly in algebraic geometry. Calculation of some morphisms will be presented between objects in D*(A) as elements in appropriate cohomology groups along with their compositions with the help of Yoneda construction under the assumption that the homological dimension of D*(A) is greater than or equal to 2. These computational settings will then be considered under sheaf cohomological context with a particular case from projective geometry.