The generalized-smooth-spaces tag has no wiki summary.

**1**

vote

**0**answers

66 views

### Relationship between tangent spaces and tangent categories for smooth topoi

Let $\mathscr E$ be a smooth topos, where I am using the terminology of nLab. In particular that imples the existence of a line object $R$ and an "infinitesimally thickened point", which is an object ...

**0**

votes

**2**answers

394 views

### Are exotic spheres still exotic in generalised smooth spaces?

This is really more of a philosophical question, and the title is somewhat rhetorical:
Exotic spheres are a feature of smooth manifold theory, where certain spheres can have more than one ...

**1**

vote

**2**answers

192 views

### are immersions/submersions captured in generalised smooth spaces by some universal property?

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 ...

**3**

votes

**0**answers

206 views

### Regular maps between Frechet manifolds and pullbacks

An oft-used example of a regular map of finite-dimensional smooth manifolds is a submersion. We have the well-known result that the pullback of a submersion exists and is a submersion. For Frechet ...

**3**

votes

**1**answer

187 views

### Can ordinary schemes be described as sheves of algebras/models for a certain Lawvere theory?

Consider the definition of a $\mathcal{C}^{\infty}$-scheme given in Dominique Joyce's "Algebraic geometry over C-infty rings". As far as I uderstand (not being an expert either in C-infty rings nor in ...

**14**

votes

**2**answers

820 views

### Nice application of generalized smooth spaces

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 ...