nLab
bicartesian closed preordered object
Contents
Context
Relations
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
-Category theory
Contents
Idea
The notion of a bicartesian closed preordered object or Heyting prealgebra object is the generalization of that of bicartesian closed preordered set or Heyting prealgebra as one passes from the ambient category of sets into more general ambient categories with suitable properties.
Definition
In a finitely complete category , a bicartesian closed preordered object or Heyting prealgebra object is a bicartesian preordered object
with a morphism and functions
such that for all global elements and ,
See also
Last revised on July 17, 2022 at 06:36:01.
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