In TeXlyre, two coauthors edit the same LaTeX or Typst file at once, and the PDF compiles inside the browser tab instead of on someone else's server. Start from a template: arXiv preprint, IEEE paper, Tufte book, Beamer deck. pdfTeX, XeTeX, and LuaTeX compile with BibTeX and Biber. Errors turn into readable cards that jump to the failing line. Live cursors show who is typing where. A shared link brings coauthors in, no accounts needed. Chat sits beside the editor, and comments can be discussed and resolved. Tracked insertions and deletions land in a review panel to accept or reject. Draw.io and TikZ editors open inside the project for shared diagrams. MathLive edits a formula under the cursor with a virtual keyboard. A bibliography panel tidies BibTeX, matches DOIs, and imports from Zotero and OpenAlex. Large files travel straight from one collaborator's browser to another. Projects export as ZIP, sync to a local folder, or back up to GitHub, GitLab, Gitea, and Codeberg. Vim, Emacs, and Helix keybindings are one setting away. The app installs as a progressive web app and works offline. Language servers like LTeX LS Plus, Harper, and Tinymist plug in through recipes beside your own signaling and TeX Live package servers. Running on a dedicated VPS on RepoCloud with guaranteed CPU, RAM, and SSD, full root SSH access, and a browser serial console. AGPL-3.0 licensed.