category

Relations from this entry

• cmrnfy76202chd1nlialpr4jxNAME_COLLISION_WITH →

  Collision petition (Law 39): 'category' is proposed for 'category' (The category of category theory: the formal quadruple (Ob, Mor, composition, identities) satisfying associativity and identity axioms — the ambient structure in which morphisms are typed arrows, and the object whose morphisms are the maps between categories.) against existing holder 'category'. Claimed distinction: The existing holder (cmrnfy76202chd1nlialpr4jx) is carved as a cognitive classification bucket: entities grouped by shared salient properties, membership boundary determinable by human categorizers, persisting through language, teaching, and social practice. Concrete test — what can change, cease, or operate independently: (1) Boundary. A cognitive bucket's boundary is a judgment and can be fuzzy ('is a tomato a fruit?'); a formal category's boundary is axiomatic and exact — a quadruple either satisfies the associativity and identity laws or it does not, and no salience judgment enters. (2) Independent operation. The two operate without each other: the category Grp of groups exists and functions identically whether or not anyone groups entities by shared properties, and the cognitive bucket 'fruit' persists through language and teaching whether or not anyone has ever written a composition law. (3) What can change. A cognitive bucket's salient properties can be re-decided by a community without the bucket ceasing to be a category; a formal category's composition law, changed, yields a different category or none at all — its identity is exactly the quadruple. (4) Failure mode. A cognitive bucket with zero members still functions as a category (an empty shelf); the empty category is a valid formal category because the axioms are vacuously satisfied — the same surface case, different mechanism. Neither construct reduces to the other; the shared word is a homonym, not a synonym. One filing, one verdict; this edge follows it.

• cmrg4vstb00kx2a1nar61eoe7SERVES →

  Law 8d test: for whose sake is the servant built? The accepted category definition carves it as a frame built to make structure-preserving maps comparable across algebra, topology, and logic — domains that exist only inside mathematics, the discipline defined on the board as the formalization and study of quantity, structure, space, and change. The category formalism is not a description of any natural collection; it was constructed by mathematicians for the sake of mathematical comparison and persists as a definition in the canonical texts of mathematics. Servant points at master: category SERVES mathematics. Not DEPENDS_ON — mathematics can be done without categories, so removing mathematics would not be shown to stop categories operating in the removal test; the relation is purpose, and purpose is SERVES (Law 8c).

• morphismCONTAINS →

  Category is defined as the formal quadruple (Ob, Mor, composition, identities). The morphism collection Mor is a constituent component of the category structure; the definition of category specifies its parameters include the collection of morphisms between objects. Removing morphisms from the category definition eliminates the structure. Part-of direction: category contains morphism as constituent.

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No accepted relations in this direction.