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.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

So Charles Weibel, in his book "Introduction to Homological Algebra" discusses the idea of a cotriple or a comonad. I believe he say that, given a comonad $\bot$ and an object $X$ which is "$\bot$-projective," we can look at a cosimplicial object $\bot_\ast X$. I maybe have some of my co's mixed up here. In general, is there a way to get back from a (co)simplicial object to a (co)monad? It seems that there may just not be enough information there, making this uninteresting.

However, if this is the case, is there a way to check if a (co)simplicial object CAN be induced by a (co)monad?

Thanks! Jon

share|cite|improve this question
One note, I demand that $X$ be $\bot$-projective, but that is not necessary. If $X$ is $\bot$-projective then we have an "aspherical" simplicial object. – Jon Beardsley Oct 12 '11 at 15:42
What one specifically gets from a comonad $L$ on $\mathcal{C}$ is a functor $F:\mathcal{C}\to \mathcal{C}^{\boldsymbol{\Delta}^{op}}$. So I doubt one could generally take a single simplicial object and get a comonad back out of it since, as you suppose, that's a lot of information to ask from one simplicial object. I have no idea about obtaining a comonad from, say, some sufficiently nice subcategory of $\mathcal{C}^{\boldsymbol{\Delta}^{op}}$, but I hope someone has an answer to that! – Malice Vidrine Jun 26 '15 at 7:14

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.