(co)limits in the category of diffeological spaces vs. category of smooth manifolds I am wondering which (co)limits that exist in the category of smooth manifolds are preserved by the inclusion into the category of diffeological spaces? Are there any results that allow us to determine which (co)limits will be preserved? Are there any examples where the manifold (co)limit differs from the corresponding diffeological (co)limit, and the latter is more "right" or "wrong" from a geometric perspective?
I have just recently picked up the book on diffeological spaces by Patrick Iglesias-Zemmour, so I am not very familiar with the theory yet. 
(Crosspost to mathoverflow)
 A: The sheaf condition in the definition of a diffeological space should imply that the inclusion functor $\mathsf{Man} \hookrightarrow \mathsf{DiffLo}$ preserves finite coproducts and Hausdorff pushouts along open embeddings. It also preserves infinite coproducts, if you replace "second countable" by "paracompact" in the definition of a manifold, which is quite natural.
Let's see if the functor preserves epimorphisms. Take for instance any proper dense open subset $U \hookrightarrow X$ of a manifold (for example, $U$ could be the complement of finitely many points, if $X$ has positive dimension; perhaps all examples are of this form?). This is an epimorphism of manifolds, basically because manifolds are (usually) assumed to be Hausdorff. The induced map of diffeological spaces is an epimorphism if and only if the restriction map $Y(X) \to Y(U)$ is injective for every diffeological space $Y$. The axioms of a diffeology don't seem to imply that this is true, basically because diffeological spaces are not assumed to be Hausdorff, right? In fact, consider the diffeological space $X \sqcup_U X$ (pushout taken in $\mathsf{DiffLo}$). Then the two inclusions $X \rightrightarrows X \sqcup_U X$ agree on $U$, but they do not agree on $X$. Thus, $\mathsf{Man} \hookrightarrow \mathsf{DiffLo}$ does not preserve the epimorphism $U \to X$. In other words, it does not preserve the pushout square of manifolds
$$\begin{array}{cc} U & \rightarrow & X \\ \downarrow && \downarrow \\ X & \rightarrow & X. \end{array}$$
It should be clear that $\mathsf{Man} \hookrightarrow \mathsf{DiffLo}$ preserves finite products. (Note: I am not 100% sure about all this, because I have read the definition of a diffeological space only yesterday.)
