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The category theoretical definition of stacks (as given for instance in Giraud: Cohomologie non-abélienne) allow for arbitrary categories as targets (the stack condition only involves isomorphisms how …

For purposes not obviously related to the question we (Ekedahl and Salomonsson - Strict polynomial functions and multisets) considered the following definition of maps of (finite) multisets: In the ca …

The empty set is known as a pseudo-torsor (the only one not a torsor if the base as here consists of single point). The reason why it is excluded is that torsor is really a relative notion, a map $X\t …

It depends completely on what you mean by cofibrations. The choice is not quite simple to make as the homotopy category of real commutative dga's is anti-equivalent to "real homotopy" which would sugg …

I move this to a more proper answer to discuss some subtle points of the question. The Eckman-Hilton argument (or more concrete calculations) shows, as Chris points out, that $\mathrm{Ext}(A,A)$ is co …

Not quite, you may have two distinct objects in the category that are isomorphic so what you get is a relation which does not have $x\leq y\wedge y\leq x\implies x=y$. However you get a well-defined p …

The value of $L$ on the element $[n]\in\Delta$ is, by Yoneda's lemma, equal to the set of morphisms $[n]\rightarrow L$, i.e., the set of subobjects of $[n]$. Such a subobject $S$ is generated by the n …

I think that the relation is that if $\psi\colon A \to TM$ is the action of the algebroid, then we have that $df(a)=\psi(a)(f)$ for $f$ in degree zero of the CE complex and $a\in\Gamma(A)$ and $d\omeg …

After some thought my pessimism (as expressed in my concurrence with the answer of Milne) has abated somewhat. If I were bold enough I would conjecture the following (assuming that the characteristic …

If what you mean by "the category of topological spaces" is the category whose objects are pairs $(S,T)$ where $S$ is a set and $T$ is a topology on $S$ and by topological space you mean a pair $(S,T …