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 $\mathbf{Cone} \left({D}\right)$.

There is believed to be a mistake here, possibly a typo. In particular: A limit for $D$ is an object in $\mathbf C$, isn't it? If yes, then this definition is formally wrong. A terminal object in $\mathbf{Cone} \left({D}\right)$ is a pair of such an object and a morphisms. Concretely, $\paren {\varprojlim_j D_j, \sequence {p_j}_j }$ is the terminal object in $\mathbf{Cone} \left({D}\right)$. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by reviewing it, and either correcting it or adding some explanatory material as to why you believe it is actually correct after all. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Mistake}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

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