# Minimality Notions via Factorization Systems

@article{Wimann2021MinimalityNV, title={Minimality Notions via Factorization Systems}, author={Thorsten Wi{\ss}mann}, journal={ArXiv}, year={2021}, volume={abs/2106.07233} }

For the minimization of state-based systems (i.e. the reduction of the number of states while retaining the system’s semantics), there are two obvious aspects: removing unnecessary states of the system and merging redundant states in the system. In the present article, we relate the two aspects on coalgebras by defining an abstract notion of minimality. The abstract notion minimality and minimization live in a general category with a factorization system. We will find criteria on the category…

## One Citation

### Minimality Notions via Factorization Systems and Examples

- Computer Science, MathematicsArXiv
- 2022

The two minimization aspects on coalgebras are related by defining an abstract notion of minimality and it is seen how the two aspects of minimization interact and under which criteria they can be sequenced in any order, like in automata minimization.

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