nLab
weakly initial object
Contents
Context
Category theory
category theory
Concepts
Universal constructions
Theorems
Extensions
Applications
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
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 November 1, 2022 at 12:52:00.
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