Given a based simplicial group, you can find its reduced homology with coefficients in a field, homotopy, and geometric realization. These are functors. If I have a free product of based simplicial groups, does these associated functors split into coproducts? More generally, does these functors preserve colimits?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
Here's how it works:
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
The answer to all of your questions is "yes", in general, if you're talking about filtered colimits -but the free product is NOT a colimit of that kind. More specifically,