6 problems

Christensen–Wu conjecture. For every diffeological space $X$ and basepoint $x$, one has

Let ${\mathcal{D}}$ be the category of diffeological spaces. Wu and Christensen-Wu define fibrations, cofibrations, and weak equivalences using affine $p$-spaces in place of the to…

Scalar multiplication conjecture. For every $r\in\mathbb{R}$, the induced map is scalar multiplication by $r$:

Let $X$ be a cofibrant diffeological space and let $Y$ be a fibrant diffeological space. Equip $C^\infty(X,Y)$ with the diffeology of smooth maps. Fibrancy conjecture for smooth ma…

Let a smooth manifold be regarded as a diffeological space, and let cofibrancy refer to the cofibrations defined using the smooth singular adjunction in the paper. Cofibrancy conje…

Let $\mathfrak{D}\mathrm{iff}$ be the category of diffeological spaces, with weak equivalences and fibrations detected by the smooth singular functor and cofibrations defined by th…