categoryConcept_count
plain-language theorem explainer
The theorem establishes that the inductive type of category concepts has cardinality five. Researchers connecting configuration dimension to category theory within Recognition Science would cite this enumeration result. The proof is a one-line decision procedure that confirms the Fintype cardinality by exhaustive enumeration of the constructors.
Claim. The finite cardinality of the set of category concepts is $5$, where the concepts are the object, the morphism, the functor, the natural transformation, and the limit or colimit.
background
The module introduces category theory core concepts derived from configDim, equating five canonical constructs to dimension D = 5. The inductive type CategoryConcept enumerates these primitives as object, morphism, functor, naturalTransformation, and limitColimit, with derived instances for DecidableEq, Repr, BEq, and Fintype. This supplies the finite set whose cardinality is asserted by the theorem, resting directly on the upstream inductive definition.
proof idea
The proof is a one-line wrapper that invokes the decide tactic to verify Fintype.card CategoryConcept = 5 by checking the five constructors of the inductive type.
why it matters
This result supplies the five_concepts field inside the CategoryTheoryCert definition, which certifies the category theory layer of the Recognition Science mathematics. It instantiates the configDim = 5 assignment for these constructs, aligning with the framework's use of dimension parameters to derive structures from the forcing chain.
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