nLab
join-semilattice object
Contents
Context
Relations
Category theory
category theory

Concepts
Universal constructions
Theorems
Extensions
Applications
Limits and colimits
limits and colimits

1-Categorical
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

2-Categorical
(∞,1)-Categorical
Model-categorical
$(0,1)$ -Category theory
Contents
Idea
The notion of a join-semilattice object is the generalization of that of join-semilattice as one passes from the ambient category of sets into more general ambient categories with suitable properties.

Definition
In a finitely complete category $C$ , a join-semilattice object is a cocartesian monoidal preordered object that is also a partially ordered object .

See also
Last revised on May 14, 2022 at 11:51:34.
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