Proposition. Let θ : ΩA → ΩB be a map of differential graded algebras, and (Hom A (B, M), ∇ θ 0 ) be a hom-connection (with respect to ΩB ) induced from a homconnection ∇ 0 : Hom A (Ω 1 A, M) → M as in 2.11. Denote by F the curvature of In particular, if ∇ 0 is flat, then so is ∇ θ 0. Proof. Note that, in view of the definition of the action of the differential graded algebra ΩB on the space n=0 Hom B (Ω n B, M) (see 3.1), the definition of ∇ θ 0 in Corollary 2.11 can be equivalently written as ∇ θ 0 (f )(b) = ∇ 0 (f b • θ) − f (db). The higher hom-connections ∇ θ n associated to ∇ θ 0 are defined as in 3.1. This definition of ∇ θ 1 together with the definition of ∇ θ 0 and with the Leibniz rule for d imply, for all b ∈ B, ω ∈ Ω 1 B and f ∈ Hom B (Ω 2 B, Hom A (B, M)) ≃ Hom A (Ω 2 B, M), Identifying Hom B (Ω 2 B, Hom A (B, M)) with Hom A (Ω 2 B, M), one thus obtains (3.8.1) ∇ θ 1 (f )(ω) = ∇ 0 (f ω • θ) + f (dω). Starting with the just derived equality (3.8.1) and then using the fact that θ is a map of differential graded algebras and the definition of ∇ 1 in terms of ∇ 0, one computes, for all ω ∈ Ω 1 A and f ∈ Hom A (Ω 2 B, M),. Therefore, (3.8.2) ∇ θ 1 (f ) • θ = ∇ 1 (f • θ). With these formulae at hand one computes the curvature of ∇ θ 0 as follows: The second equality follows by the definition of ∇ θ 0 in 2.11, the third equality is a consequence of (3.8.1). Since ∇ θ 1 arises from the hom-connection ∇ θ 0, it satisfies the Leibniz rule in Lemma 3.2. This yields the fourth equality. The penultimate equality follows by (3.8.2). This proves the first assertion of the proposition. The second assertion is immediate. ⊔ ⊓ 3.9. A differential graded algebra ΩA is said to be semi-free if Ω n+1 A = Ω n A⊗ A Ω 1 A, for all n ≥ 1. As revealed in [15], there is a bijective correspondence between semi-free differential graded algebras over A and A-corings with a group-like element. Starting with an A-coring C [16] with coproduct ∆ : C → C⊗ A C, counit ε : C → A and a grouplike element x ∈ C, the associated differential graded algebra ΩA C,x is determined from Ω 1 A C,x := ker ε, with the differential for all a ∈ A, c ∈ ker ε.<issue_start><issue_comment>Title: [expo] Remove most expo-* packages from expo package
username_0: # Why

In SDK33 we deprecated imports from the Expo package, instead users install them separately, eg: `expo install expo-sensors`. This has many benefits that we're already aware of that I'm not going to repeat here for brevity. 

# How

I removed the dependencies and tested in a local bare project to ensure that the project would build and run in Xcode and also that it would work in the Expo client.

I had to keep some of the unimodule dependencies around because they are used by parts of the expo package in a way we can't remove (globals, for example).

# Test Plan

You can install `expo@34.0.0-experiment.6` to a bare project and give it a try!

# Checklist

- [x] Verify it works as expected in bare on iOS and Android
- [x] Verify it works as expected in managed on iOS and Android
- [x] Verify it works for web
- [x] Add docs for community native modules we include now that they can't be imported from the expo package
- [ ] Create a package for the `Google.ts` file so it doesn't need to live in the `expo` package and force a dependency on `expo-app-auth`

# Followup

- @EvanBacon is planning on removing maps related code from the package and into something like `expo-maps`
<issue_comment>username_0: Client workflow failure is unrelated :O
<issue_comment>username_0: need to look into why web storybook failed, I think it's because of SVG being removed from expo
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