Sure, I have adjusted the wording.

But the exposition of this whole proposition leave much room for improvement. You should feel invited to edit it or re-write it from scratch.

]]>This formulation is really misleading. It is not difficult to construct examples of categories without limits in which every coslice does have a limit, e.g. finite sets with surjections.

It would be proper, in my opinion, to remove it, leaving only the "precisely"-part, or reformulate:

Proposition 3.1. If limits exist in the underlying category then the same is true for every under category and these limits coincide.

Rostislav Matveev ]]>

copied over, from *overcategory*, statement and proof of computing limits in undercategories