Monomorphisms, epimorphisms, (co-)images and factorizations in $\infty$-categories Several of the many notions that don't work the same way when passing to $\infty$-categories are the ones mentioned in the title. I'm trying to understand the conceptual picture around these notions in the world of higher category theory (conceptual answers will be more useful to me than model specific answers).
My question are conceptually very simple:

  
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*What are ($n$-?)monomorphisms and ($n$-?)epimorphisms in an $\infty$-catgory? What are the fundamental differences with $1$-categories?
  
*What are ($n$-?)coimages and ($n$-?)-images in an $\infty$-category? (it seems that on n-lab the definitions for both of them [1] [2] are exactly the same which is very confusing) What are the fundamental differences with $1$-categories? Which of these coincides with the Postnikov decomposition in $\infty$-groupoids? 
  
*What is an $n$-ary factorization system for an $\infty$-category? Is this a direct analog of epi-mono factorization? If so In what sense?
  

I could elaborate but I tried and concluded that it will probably only serves to confuse me and the readers. I'm still confused by many of these notions. 
 A: I can answer to 4: https://arxiv.org/abs/1501.04658 here the definition is given for a generic poset $J$, provided it has a monotone $\mathbb{Z}$-action.
For 1,2,3 and the preamble, I think that the theory of factorization systems is pretty much unchanged from 1-category theory: see here; the same theorems hold, provided you translate them into quasicategorical terms (this is phrased in a specific model, and yet it is maybe possible to write it up model-independently -doing so in a few specific examples is part of my current plans :-) ).
What changes, when you upgrade to $(\infty,1)$-categories, is the fact that $(Epi, Mono)$ on $\bf Set$ is no longer the most natural example, replaced by $(n\text{-}Epi, n\text{-}Mono)$ on $\infty\text{-}\bf Gpd$.
Notice that all I'm saying is true for $(\infty\color{red}{,1})$-categories only, not $(\infty,n)$-categories, not $(\infty,\infty)$-categories.
A: An $n$-monomorphism is a map $A\to B$ for which $Map(X,A)\to Map(X,B)$ has all homotopy fibers $n$-truncated, for all $X$; a space (=$\infty$-groupoid) is $n$-truncated if its homotopy groups all vanish in dimensions $>n$.
An $n$-epimorphism is an $n$-monomorphism in the opposite $\infty$-category.
When $n=-1$ you recover Denis's definition of monomorphism and epimorphism: note that a space is $(-1)$-truncated if and only if it is empty or contractible.
The phenomenon of "$n$-epi/mono factorization" in an $\infty$-category does not actually involve factorization as ($n$-mono)($n$-epi), but rather as ($n$-mono)($n$-connected map).  The class of $n$-connected maps is usually defined as a kind of left complement to $n$-monomorphisms, so the existence of such factorizations is basically the assertion that your $\infty$-category admits a factorization system where the right-class is the class of $n$-monos.  (These exist in all "reasonable" examples, e.g., presentable $\infty$-categories.)
This same issue shows up in 1-category theory: epi/mono factorization tends to be rare, and more commonly one considers factorizations of the form: (regular epi)(mono).
The factorization ($n$-mono)($n$-connected) can be thought of as factorization through an "$n$-image".  It is clearly not a self-dual notion, hence there is a dual but distinct notion of factorization through an "$n$-coimage".
