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Martin Sleziak
Martin Sleziak
7:03 AM
I have edited this question in the same way - to be consistent with the way this tag was treated in the past.
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Q: How the map in proving the direct limit property $\lim\limits_{\to}(M_i\times N)\cong(\lim\limits_{\to}M_i)\times N$ is well defined

Soham ChatterjeeI want to show the direct limit of $(M_i\times N,\mu_{ij}\times id_N)$ is $M\times N$ where $M$ is the direct limit of $(M_i,\mu_{ij})$. Suppose $Q$ be any $R-$ module. Let $\alpha_i:M_i\times N\to Q$ be a collection of $R-$linear maps. Then for all $i\leq j$ we have $$\alpha_i=\alpha_j\circ (\mu...

modules limits-colimits
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A: Tag management 2015

Asaf KaragilaUpdate: The tag limits-colimits was created by Martin. So it seems that the best course of action is now to merge these two tags, or add them as synonyms. Do we need the direct-limit and inverse-limits? I have no opinion on the matter, but maybe those should be merged into a single tag someho...

I don't think we need these tags, just like we don't need tags like "coproduct", "equalizer" and every possible (co)limit shape one can think of -- that's way too many tags for a very limited payoff (if there's a payoff at all, I can't think of any). — Najib Idrissi Jul 24, 2015 at 9:13
I think making both direct-limits and inverse-limits a synonym of limits-colimits would make sense. — Najib Idrissi Jul 29, 2015 at 18:12
 

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