Correlations of multiplicative functions in function fields

We develop an approach to study character sums, weighted by a multiplicative function $f:\mathbb{F}_q[t]\to S^1$, of the form \begin{equation} \sum_{G\in \mathcal{M}_N}f(G)\chi(G)\xi(G), \end{equation} where $\chi$ is Dirichlet and $\xi$ short interval over $\mathbb{F}_q[t].$ then deduce versions Matom\"aki-Radziwill theorem Tao's two-point logarithmic Elliott conjecture fields $\mathbb{F}_q[t]$, $q$ fixed. The former these improves on work Gorodetsky, latter extends Sawin-Shusterman correlations M\"{o}bius for various values $q$. Compared with integer setting, we encounter different phenomenon, specifically low characteristic issue in case that power $2$. As application our results, give proof field version K\'atai classifying functions small increments, classification obtained being from case. In companion paper, use results characterize limiting behavior partial sums particular solve "corrected" Erd\H{o}s discrepancy problem $\mathbb{F}_q[t]$.