Let $T$ be a monad on a [concrete category][1] $\mathcal{C}$, and $A$ an algebra over $T$. The [bar construction][2] is a simplicial object in the category $\mathcal{C}^T$ of algebras which we can think of a sort of "resolution" of $A$. Some of the arrows look like the following diagram:
$$
\begin{array}{ccc} 
\cdots TTA \rightrightarrows TA \to A
\end{array}
$$
(I unfortunately cannot draw more arrows here. See the link above for a better picture.)

Now, is such a simplicial object a [Kan complex][3], or at least a [quasicategory][4]? Is there a filling condition for horns, in general? If not, what would be a counterexample? 

Any reference would also be welcome. 


  [1]: https://ncatlab.org/nlab/show/concrete+category
  [2]: https://ncatlab.org/nlab/show/bar+construction
  [3]: https://ncatlab.org/nlab/show/Kan+complex
  [4]: https://ncatlab.org/nlab/show/quasi-category