The following result should be obvious.

Proposition: Convenient vector spaces are microlinear.

Corollary: C^{∞}-manifolds are microlinear.

Proposition: If X is a Weil exponentiable and microlinear Frölicher space, then so is X ⊗ W for any Weil algebra W.

We note in passing that microlinearity is closed under transversal limits.

Let X be the limit of the diagram F, i.e., X = Lim F

Let W be the limit of an arbitrarily given finite diagram D of Weil algebras, i.e.,

[since Lim F is the transversal limit] = Lim_{F} Lim_{D} (F ⊗ D)

[since double limits commute] = Lim (F ⊗ (Lim D))

[since every object in F is microlinear] = Lim (F ⊗ W )

[since Lim F is the transversal limit] = X ⊗ W

Therefore we have the desired result.

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