The limit of a diagram indexed by the category $\bbomega^\mathrm{op}$ is called an inverse limit of a tower or a sequence of morphisms. On account of this example, the term inverse limit'' is sometimes used to refer to limits of any shape. A diagram indexed by $\bbomega^\mathrm{op}$ consists of a sequence of objects and morphisms\n$$ \xymatrix{ \cdots \ar[r] & F_3 \ar[r] & F_2 \ar[r] & F_1 \ar[r] & F_0}$$ together with composites and identities, which are not displayed. A cone over this diagram is an extension of this data to a diagram of shape $(\bbomega +1)^\mathrm{op}$. Explicitly, a cone consists of a new objectall the way to the left’’ together with morphisms making every triangle commute:\n\(\xymatrix@=35pt{ c \ar[d]^\cdots \ar[dr]\mid{\colorbox{white}{\makebox(9,5){\scriptsize$\lambda_{3}$}}} \ar[drr]\mid{\colorbox{white}{\makebox(9,5){\scriptsize$\lambda_{ 2}$}}} \ar[drrr]\mid{\colorbox{white}{\makebox(9,5){\scriptsize$\lambda_{ 1}$}}} \ar[drrrr]\mid{\colorbox{white}{\makebox(8,4){\scriptsize$\lambda_{ 0}$}}} \\ \cdots \ar[r] & F_3 \ar[r] & F_2 \ar[r] & F_1 \ar[r] & F_0}\) The inverse limit, frequently denoted by $\varprojlim F_n$, is the terminal cone. Similar remarks apply with any limit ordinal $\bbalpha$ in place of $\bbomega$.