The fibre-products tag has no usage guidance.

**2**

votes

**0**answers

86 views

### Non-clean fiber products

Usually, the most general condition for fiber product of manifolds (or vector bundles) to exist is that we require the images cleanly intersects. See e.g.
When do fibre products of smooth manifolds ...

**4**

votes

**2**answers

418 views

### Isomorphism type of fibered products of groups

This question is, in a way, a follow-up of this earlier question of mine.
Background
Let $A$, $B$ and $F$ be finite groups and let $\alpha: A \to F$ and $\beta: B \to F$ be surjective homomorphisms.
...

**1**

vote

**1**answer

272 views

### Expressing fiber product of affines via an ideal

Let $X$ (resp. $Y$) be the affine $k$-scheme defined by the ideal $I$ (resp. $J$) in the polynomial ring $k[x_1,...x_n]$ (resp. $k[y_1,...,y_m]$).
Let $Z$ be the affine scheme defined by the ideal ...

**12**

votes

**2**answers

2k views

### When do fibre products of smooth manifolds exist?

Harold asks what conditions on $f:M\to L$ and $g:N\to L$, both smooth maps of smooth manifolds, ensures the existence of the fibre product $M \times_L N$.