cathedral = sandbox env in the provider's cloud, so [codex](https://chatgpt.com/codex) uses this model. Their codex-cli product is the Bazaar model, where you run in your computer, in your own environment.
Claude Code, on the other hand, doesn't have the cloud-based sandboxing product, you have to run in on your computer, so the bazaar model. You can also run in in a way that anthropic never envisioned (e.g. give it control to your house). Curser also follows the same model, albeit they have been trying to get into the cathedral model by using the background agent (as someone also pointed out below). Presumably not to lose the market share to codex/jules/etc.