# Questions tagged [limits-colimits]

For questions about categorical limits and colimits, including questions about (co)limits of general diagrams, questions about specific special kinds of (co)limits such as (co)products or (co)equalizers, and questions about generalizations such as weighted (co)limits and (co)ends.

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### References for Learning Inverse Limits (for Profinite Groups)

I'm doing some independent study on Profinite Groups this summer and, as I understand it, it is important to be familiar with the notion of an inverse limit before doing so. The trouble for me is that ...
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### If one vertical arrow in a pullback is an iso, then so is the other

Consider the pullback square: $\require{AMScd}$ \begin{CD} A @>f>> B\\ @Vg VV @VV h V\\ C @>>j > D \end{CD} Suppose $h$ is an isomorphism. I'm trying to show that $g$ ...
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### Do people use other limits than products, equalizers and pullbacks?

This is a somewhat vague question. I've seen several introductions to category theory, and when someone presents (co)limits, the typical examples are always (co)products, (co)equalizers and pullbacks/...
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### Fundamental Group functor has no left Adjoint

I have a question about a remark done by Martin Brandenburg on Tyler Lawson's answer in this MO discussion: https://mathoverflow.net/questions/10364/categorical-homotopy-colimits/10399#10399 The ...
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### Proving that $p_I\circ h=p_I\circ h'$ implies $h=h'$
An exercise from Leinster: I was wondering if my solution is correct? (a) Assume $h,h':A\to L$ are arrows such that $p_I\circ h=p_I\circ h'$ for all $I$. Define $f_I=p_I\circ h$, as shown on the ...