nLab
semilattice object

Contents

Context

Algebra

Category theory

Contents

Idea

The notion of a semilattice object is the generalization of that of semilattice as one passes from the ambient category of sets into more general ambient categories with suitable properties.

Definition

In a symmetric monoidal category with diagonals (C,,I,Δ ())(C, \otimes, I, \Delta_{(-)}), a semilattice object is a commutative monoid object (M,μ,η)(M, \mu, \eta) such that for every morphism a:IMa:I \to M, μΔ Ma=a\mu \circ \Delta_M \circ a = a, where Δ M\Delta_M is the diagonal morphism of MM.

See also

Last revised on May 14, 2022 at 12:26:13. See the history of this page for a list of all contributions to it.