Category:Definitions/Limits and Colimits

This category contains definitions related to limits and colimits in the context of Category Theory.
Related results can be found in Category:Limits and Colimits.

Let $\mathbf C$ be a metacategory.

Let $D: \mathbf J \to \mathbf C$ be a $\mathbf J$-diagram in $\mathbf C$.

Let $\mathbf{Cone} \left({D}\right)$ be the category of cones to $D$.

A limit for $D$ is a terminal object in $\mathbf{Cone} \left({D}\right)$.

It is denoted by $\varprojlim_j D_j$; the associated morphisms $p_i: \varprojlim_j D_j \to D_i$ are usually left implicit.