A sequential (co)limit is a limit/colimit whose diagram category is a nonzero ordinal or its opposite (regarded as a poset, regarded as a category). For instance over a tower diagram.
Sometimes the term is used even more specifically for a (co)limit over the ordinal $\omega$.
Thus, a sequential limit is a special case of a directed limit. See there for more details.
Discussion of sequential colimits (in the generality of homotopy colimits) in homotopy type theory:
It could also be found in section 26 of the draft of the textbook:
Last revised on October 3, 2023 at 01:33:19. See the history of this page for a list of all contributions to it.