TITLE: Name of "slice" category with 2-cells as morphisms ?
QUESTION [5 upvotes]: Hi,
I would like to know whether there is a standard name for the following "slice" category:
Let $\mathcal{C}$ be a 2-category and $c \in \mathcal{C}$ an object of $\mathcal{C}$.
We can form the category where an object $(d,f)$ is a pair of an object $d\in\mathcal{C}$ and an
arrow $f : d\to c$. A morphism $(h, \alpha)$ from $(d,f)$ to $(e,g)$ is given by
$h : d \to e$ and a 2-cell $\alpha : f \Rightarrow g \circ h$.
Thanks a lot,
ben
[Edit: fixed typo mentioned by Martin]

REPLY [2 votes]: See this answer to much the same question.  I would call this the 'lax' slice category, although it's not so common a notion that everyone would know what you meant, so maybe you should keep the scare quotes around 'lax'.
A propos of Martin's comment, the correct notion of slice 2-category depends on what you're doing -- you might want the strict version, with strictly commuting triangles, or the pseudo version, with invertible 2-cells (this is the strictest one that makes sense for non-strict 2-categories), or this lax version.  Or you might want to restrict to (discrete) (op)fibrations as objects.