nLab
bi-initial object
Redirected from "initial object in a bicategory".
Contents
Context
2-Category theory
2-category theory
Definitions
Transfors between 2-categories
Morphisms in 2-categories
Structures in 2-categories
Limits in 2-categories
Structures on 2-categories
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
Idea
Bi-initial objects are the bicategorical analogues of initial objects in categories.
Definition
In a bicategory , an object is bi-initial (or biinitial) when for all , there is an equivalence of categories between and the terminal category with a single object and single morphism .
References
This concept appears among others in:
- Tslil Clingman, Lyne Moser, 2-limits and 2-terminal objects are too different (arXiv:2004.01313)
Last revised on October 3, 2021 at 13:14:19.
See the history of this page for a list of all contributions to it.