A simplicial set $X$ is $k$-coskeletal iff the following condition holds:

a simplex of dimension $> k$ is present iff all of its $k$-dimensional faces are present in $X$.

A standard example is the usual nerve of a small category, which is readily seen to be $1$-coskeletal. (Similarly, the nerve of an $n$-category is $n$-coskeletal).

A simplicial set $X$ is $k$-coskeletal iff the following condition holds:

a simplex of dimension $\geq k$ is present iff all of its $(k-1)$-dimensional faces are present in $X$.

A standard example is the usual nerve of a small category, which is readily seen to be $2$-coskeletal. (Similarly, the nerve of an $n$-category is $(n+1)$-coskeletal).

A simplicial set $X$ is $k$-coskeletal iff the following condition holds:

a simplex of dimension $> k$ is present iff all of its $k$-dimensional faces are present in $X$.

A standard example is the usual nerve of a small category, which is readily seen to be $1$-coskeletal. (Similarly, the nerve of an $n$-category is $n$-cosimplicial).

A simplicial set $X$ is $k$-coskeletal iff the following condition holds:

a simplex of dimension $> k$ is present iff all of its $k$-dimensional faces are present in $X$.

A standard example is the usual nerve of a small category, which is readily seen to be $1$-coskeletal. (Similarly, the nerve of an $n$-category is $n$-coskeletal).