nLab
sequential limit
Contents
Context
Limits and colimits
limits and colimits
1Categorical

limit and colimit

limits and colimits by example

commutativity of limits and colimits

small limit

filtered colimit

sifted colimit

connected limit, wide pullback

preserved limit, reflected limit, created limit

product, fiber product, base change, coproduct, pullback, pushout, cobase change, equalizer, coequalizer, join, meet, terminal object, initial object, direct product, direct sum

finite limit

Kan extension

weighted limit

end and coend
2Categorical
(∞,1)Categorical
Modelcategorical
Contents
Definition
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.
References
Discussion of sequential colimits (in the generality of homotopy colimits) in homotopy type theory:
Last revised on February 19, 2023 at 08:28:59.
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