lSpace Infinite dimensional manifolds from a new point of view (Rev #3, changes)

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On first reading, this appears to be in the same mould as diffeological spaces and Chen spaces. The basic construction is as sheaves on the category of manifolds with corners (technically, a small equivalent subcategory). This reduces to sheaves on open subsets of $\mathbb{R}^n_k$ ($k$-quadrant in $\mathbb{R}^n$). It therefore sits between diffeological spaces and Chen spaces and will have functors to each (with adjunctions) exactly as lie between diffeological spaces and Chen spaces.