nLab sequential colimit

Definition

A sequential colimit is a colimit of the diagram

$$A_0 \overset{f_0}\to A_1 \overset{f_1}\to A_2 \overset{f_2}\to \ldots$$

Thus, a sequential colimit is a special case of a directed colimit. See there for more details.

Related concepts

• sequential limit

• colimit

References

Discussion of sequential colimits (in the generality of homotopy colimits) in homotopy type theory:

• Egbert Rijke, Sequential colimits [pdf], Lecture 15 in: Introduction to Homotopy Type Theory, lecture notes, CMU (2018) [pdf, pdf, webpage]

It could also be found in section 26 of the draft of the textbook:

• Egbert Rijke (2022), Introduction to Homotopy Type Theory, draft. (pdf)