nLab
Boolean prealgebra object
Contents
Context
Relations
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

fibered limit
2Categorical
(∞,1)Categorical
Modelcategorical
$(0,1)$Category theory
Contents
Idea
A version of a Boolean algebra without the preorder being an antisymmetric relation, internal to a finitely complete category.
Definition
In a finitely complete category $C$, a Boolean prealgebra object is a bicartesian closed preordered object $X$ with a function
$\zeta:((* \to X) \times (* \to X)) \to (* \to R)$
such that for all global elements $a:* \to X$ and $b:* \to X$,
 $s \circ \zeta(a, b) = a \Rightarrow b$
 $t \circ \zeta(a, b) = (a \Rightarrow \bot) \vee b$
See also
Last revised on May 14, 2022 at 14:41:38.
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