Data from software repositories have become an important foundation for the empirical study of software engineering processes. A recurring theme in the repository mining literature is the inference of developer networks capturing e.g. collaboration, coordination, or communication from the commit history of projects. Most of the studied networks are based on the co-authorship of software artefacts defined at the level of files, modules, or packages. While this approach has led to insights into the social aspects of software development, it neglects detailed information on code changes and code ownership, e.g. which exact lines of code have been authored by which developers, that is contained in the commit log of software projects. Addressing this issue, we introduce git2net, a scalable python software that facilitates the extraction of fine-grained co-editing networks in large git repositories. It uses text mining techniques to analyse the detailed history of textual modifications within files. This information allows us to construct directed, weighted, and time-stamped networks, where a link signifies that one developer has edited a block of source code originally written by another developer. Our tool is applied in case studies of an Open Source and a commercial software project. We argue that it opens up a massive new source of high-resolution data on human collaboration patterns.