Reedy category¶
In mathematics, especially category theory, a Reedy category is a category R that has a structure so that the functor category from R to a model category M would also get the induced model category structure.
Core Idea¶
Reedy category is treated here as the recurring category theory identity summarized by this source-grounded definition: In mathematics, especially category theory, a Reedy category is a category R that has a structure so that the functor category from R to a model category M would also get the induced model category structure. In mathematics, especially category theory, a Reedy category is a category R that has a structure so that the functor category from R to a model category M would also get the induced model category structure.
Scope of Application¶
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Definition. Note some authors such as nlab require each factorization to be unique.
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Reedy model structure. A Reedy model structure is a canonical model-category structure placed on the functor category M^R when R is a Reedy category and M is a model category.
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Definition. A Reedy category consists of the following data: a category R, two wide (lluf) subcategories R-, R+ and a functorial factorization of each map into a map in R- followed by.
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Eilenberg–Zilber category. An Eilenberg–Zilber category is a variant of a Reedy category.
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Documented setting. In mathematics, especially category theory, a Reedy category is a category R that has a structure so that the functor category from R to a model category M would also get.
Clarity¶
A clear use of Reedy category names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In mathematics, especially category theory, a Reedy category is a category R that has a structure so that the functor category from R to a model category M would also get the induced model category structure.
Manages Complexity¶
Reedy category compresses multiple category theory details into a stable diagnostic relation. The source shows both the central mechanism—it was introduced by Christopher Reedy in his unpublished manuscript.—and the practical consequence—in mathematics, especially category theory, a Reedy category is a category R that has a structure so that the functor category from R to a model category M would also get the induced model category structure.
Abstract Reasoning¶
- Type the carrier. Identify the category theory entities to which the claim applies.
- State the relation. Use the source-grounded identity: In mathematics, especially category theory, a Reedy category is a category R that has a structure so that the functor category from R to a model category M would also get the induced model category structure.
- Check operation and conditions. Note some authors such as nlab require each factorization to be unique.
- Demand recognition evidence.
Knowledge Transfer¶
Within the home domain. Knowledge about Reedy category transfers literally when a new case preserves the same carrier type, relation, and recognition test. Note some authors such as nlab require each factorization to be unique. A Reedy model structure is a canonical model-category structure placed on the functor category M^R when R is a Reedy category and M is a model category. Beyond the home domain. No canonical parent is asserted for Reedy category.
Relationships to Other Abstractions¶
Current abstraction Reedy category Domain-specific
Parents (1) — more general patterns this builds on
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Reedy category is a kind of Category Prime
Reedy category is a domain-specific kind of category under its frozen identity and differentia. Complete-catalog comparison found the corresponding live broader identity.
Hierarchy paths (3) — routes to 3 parentless roots
- Reedy category → Category → Associativity → Invariance
- Reedy category → Category → Closure
- Reedy category → Category → Associativity → Symmetry
Neighborhood in Abstraction Space¶
Reedy category sits in a moderately populated region (57th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Formal Grammar & Syntactic Structure (16 abstractions)
Nearest neighbors
- Adequate subcategory — 0.85
- Profunctor — 0.85
- Kripke–Platek set theory with urelements — 0.85
- Conjunctive grammar — 0.85
- Subfunctor — 0.85
Computed from structural-signature embeddings · 2026-10-08