Hi there. Suppose ${\bf C}\_1$, ${\bf C}\_2$ and $\bf D$ are categories and $F\_i$ is a functor ${\bf C}\_i \to \bf D$. Consider the subcategory of the comma category $( F\_1 \downarrow F\_2)$ whose objects are all triples $(c\_1, c\_2, e)$ where $c\_i \in \mathrm{obj}(\mathbf C\_i)$, $F\_1(c\_1) = F\_2(c\_2)$ and $e$ is the identity of $\hom\_\mathbf{D}(c)$ with $c := F\_i(c\_i)$. Is there a standard name for this particular category? Thank you in advance.



Looking for the name of a particular subcategory of a comma category
The (strict) pullback of $F\_0$ and $F\_1$.


