nLab
sequential limit
Redirected from "sequential diagrams".
Contents
Context
Limits and colimits
limits and colimits
1-Categorical
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limit and colimit
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limits and colimits by example
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commutativity of limits and colimits
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small limit
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filtered colimit
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sifted colimit
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connected limit, wide pullback
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preserved limit, reflected limit, created limit
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product, fiber product, base change, coproduct, pullback, pushout, cobase change, equalizer, coequalizer, join, meet, terminal object, initial object, direct product, direct sum
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finite limit
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Kan extension
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weighted limit
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end and coend
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fibered limit
2-Categorical
(∞,1)-Categorical
Model-categorical
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 .
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:
It could also be found in section 26 of the draft of the textbook:
Last revised on October 3, 2023 at 01:33:19.
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