1id1Abstract
A token structure is a set of carrier elements together with a chosen collection of finite records over those elements and a fixed symbol alphabet, where structure-preserving maps are those functions that carry recorded tokens to recorded tokens. This survey traces the categorical treatment of such structures from four historical sources: categories of relational structures and their homomorphisms; topological and concrete categories, where morphisms are underlying functions subject to a fibrewise admissibility condition; algebraic and coalgebraic accounts of terms, term graphs, sharing and sequences; and the categorical linguistics descending from Lambek's syntactic calculus. We then describe how the Token Space framework of Pan assembles these ingredients into a single category whose objects are carriers with heaps of finite words over carrier and core symbols, and whose fibres are free quantales rather than products of powersets. For each component we state what the earlier theory already provides, what the Token Space presentation adds, and which structural questions remain open. The aim is a map of priorities and dependencies, not an evaluation of applications to machine learning.
Cite this version
Wuming Pan. Categorical Studies of Token Structures: A Historical Perspective. 1id1, v1, 26 October 2026. 1id1:core:20261026-0001@v1. https://1id1.net/id/core/20261026-0001/v1/
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The v1 publication imprint was updated on 26 October 2026 to use the date-and-sequence identifier requested by the author. The former random identifier remains a permanent alias to this record. Scholarly text, body placement and pagination are unchanged.
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