Atlas of Fundamental Concepts

© 2026 Advay Mengle · Terms · Edit me!

Graph centered on Lattice-ordered group, showing the selected concept and its surrounding relations.Preparing the interactive atlas…
Curated starting points

Stories & Views

Open the stories and views directory
Relationship-aware analysis

Compare concepts

Choose two concepts to compare or connect.
Reading the graph

Guide to the Atlas

Open full user guide

Canonical static concept record

Lattice-ordered group

Open this concept in the interactive graphRead the Markdown equivalent

Summary

A group with a lattice order invariant under translations.

Record metadata

Canonical name
Lattice-ordered group
Concept ID
lattice_ordered_group
Content version
2.3.0
Primary field
Mathematics
Fields
Mathematics
Primary domain
Order theory
Domains
Order theory, Algebra
Alternate terminology
No alternate terminology is currently authored for this record.

Carrier(s)

Axioms / constraints

Notes

Every totally ordered group is lattice-ordered, but not conversely.

Concept sources

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

group + lattice order(construction junction)Lattice-ordered group

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID
j_lgroup__out
Relation type
Combine compatible structures combine-compatible
Direction
source → target
Endpoint roles
source: Builds toward; target: Built from
Authored annotation
impose compatibility

Authored explanation

Require left and right translations to preserve the lattice order.

How to interpret this relation type

Feed several structures into a construction junction and impose compatibility between them.

Relation sources

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

No direct relations are authored in this direction.