nLab
weakly initial object
Redirected from "weak initial".
Contents
Context
Category theory
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
An object in a category is weakly initial if there exists a morphism from it to every other object in the category.
(So a weakly initial object is an actual initial object if this morphism is unique.)
Weak initiality is an instance of a weak colimit. It is also an instance of a weakly initial set that happens to be a singleton set.
References
Weak adjoint functors along with weak colimits, with weakly initial objects as a special case, were defined in:
See also:
Last revised on April 22, 2023 at 13:32:50.
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