My question is: Does the forgetful functor F:(Mfd) $\to$ (Top) preserve pullbacks? Detailed explanation is following. A pullback is defined as a manifold/topological space satisfying a universal ...
Immersions & sumersions are important in differential manifolds. They rely on their definition of the construction of the tangent bundle. I realise that generalised smooth spaces do not have a ...
Recall that when dealing with topological spaces one usually likes dealing with a subcategory of $Top$ which is convenient, one facet of which is that it is cartesian closed. However to get to a ...
The category of internal locales in the Grothendieck topos of sheaves on a locale X is equivalent to the slice category over X. In other words, internal locales over X are precisely morphisms of ...
Is the category of smooth manifolds equivalent to the opposite category of the category of commutative monoids of some additive symmetric monoidal category?
This is a followup to my previous question, which asked whether the category of commutative or noncommutative C*-algebras or von Neumann algebras is equivalent to the category of commutative or ...
I am a fan of category theory in general, and I appreciate that various brands of generalized smooth spaces (Diffeological spaces, Chen spaces, Frolicher spaces ...) form much nicer categories of ...
This question tells us that in general colimits do not exist in the category of manifolds. However, this negative answer is not very satisfying. A manifold can be considered as a colimit of its ...
This question is motivated by the recent paper An invitation to higher gauge theory by Baez and Huerta, and the 2007 paper Parallel Transport and Functors by Schreiber and Waldorf. Let $M$ be a ...
Let $G$ be a (maybe Lie) group, and $M$ a space (perhaps a manifold). Then a principal $G$-bundle over $M$ is a bundle $P \to M$ on which $G$ acts (by fiber-preserving maps), so that each fiber is a ...