# A Remark in Weibel's “Introduction to Homological Algebra”

In the section on the derived functors of the inverse limit(with $$...3\rightarrow 2 \rightarrow 1 \rightarrow 0$$ as index category), Weibel constructs the inverse limit using the map $$\Delta$$ in the photograph. Later, he remarks that everything goes through for any $$AB4*$$ category. But I can't even construct the map in the general case. My question is, how does one do this for any $$AB4*$$ category?

• The question is just about how to define $\Delta$ without elements ? This is easy then, $\Delta$ is the difference between the identity $\prod_{i\in\mathbb{N}}A_i\to\prod_{i\in\mathbb{N}}A_i$ and the map such that on the $A_j$ component, it is $\prod_{i\in\mathbb{N}}A_i\to A_{j+1}\to A_j$. – Roland Jan 6 at 12:32
• Thanks, it was so silly of me to miss that! – Jehu314 Jan 6 at 14:04