DecompositionSpaces v1.1

Revision based on comments from the referee.

Full Changelog: v1.0...v1.1

DecompositionSpaces v1.0

Submitted version

This is the submitted version and coincides with arXiv version 1. Only minor changes compared to v0.3.

Full Changelog: v0.3...v1.0

DecompositionSpaces v0.3

Updates based on feedback from readers

• Some parts of introduction are streamlined
• Removed some old comments
• Minor corrections and adjustments to awkward phrasing

Full Changelog: v0.2...v0.3

DecompositionSpaces v0.2

First complete draft

• Added an abstract and an introduction.
• Made a note about other factorization systems.
• Added definition of culf map, and briefly mention them at the ends of sections 6 and 7.

Full Changelog: v0.1...v0.2

DecompositionSpaces v0.1

Early release

This is an early snapshot of the paper. There is not yet an introduction or abstract, but the main body of the text includes the material from the original talks.