Question: What type of category does Origanum and Athyrium have in common?

Context articles: Fitkid
Category utility
Athyrium
Yoneda lemma
Athyrium filix-femina
Pot marjoram
Internal category
Origanum
Athyrium yokoscense
Retusin (flavonol)

Fitkid (also "FitKid", "Fit Kid" or "Fit-Kid") is a type of children's sport combining gymnastics, dance and acrobatics.
 It originated in Europe in the 1990s, and is meant to engage children 8–18 years of age in fun individual and group exercise, free of the extremes of more strenuous aerobics or traditional gymnastics.
 International competitions are organized regularly by the "International FitKid Division", in addition to national competitions.
 A routine stands of four types of elements: strength, flexibility, acrobatics, and jumps.
 All elements are graded by difficulty from A to H.
 A elements being worth 0.1 points, B 0.2, C 0.3, and so on until H which is worth 0.8.
 Routines get evaluated in three categories: technique, artistry, and content (execution of elements).
 Competition is divided by age groups (I. to IX.
 (or Senior in A category)), and categories ( which are based on knowledge).
 There three categories (from hardest to easiest) A, B, and C, also called Dance.
 In each categories there are group and individual routines.
 In C Category (here group routines are also called Dance Show) team member can go from 4 to 8.
 In A and B category there are duos, small groups (3-4), and big groups (5-6).
 In C category, individually 4 elements have to be performed ( one from each type), A or B difficulty, and in groups, two are optional.
 In B category individually 8 elements need to be performed ( two from each type) A-D difficulty ( but max.
 two elements can be D), and in groups 4 (same as C category individual).
 In A category team and individual, 8 elements need to be performed (same as B category) and an acrobatic connection is optional.
 Skills in A category can be any difficulty.
Category utility is a measure of "category goodness" defined in and .
 It attempts to maximize both the probability that two objects in the same category have attribute values in common, and the probability that objects from different categories have different attribute values.
 It was intended to supersede more limited measures of category goodness such as "cue validity" (; ) and "collocation index" .
 It provides a normative information-theoretic measure of the "predictive advantage" gained by the observer who possesses knowledge of the given category structure (i.e., the class labels of instances) over the observer who does "not" possess knowledge of the category structure.
 In this sense the motivation for the "category utility" measure is similar to the information gain metric used in decision tree learning.
 In certain presentations, it is also formally equivalent to the mutual information, as discussed below.
 A review of "category utility" in its probabilistic incarnation, with applications to machine learning, is provided in .
Athyrium (lady-fern) is a genus of about 180 species of terrestrial ferns, with a cosmopolitan distribution.
 It is placed in the family Athyriaceae, in the order Polypodiales.
In mathematics, specifically in category theory, the Yoneda lemma is an abstract result on functors of the type "morphisms into a fixed object".
 It is a vast generalisation of Cayley's theorem from group theory (viewing a group as a particular kind of category with just one object).
 It allows the embedding of any category into a category of functors (contravariant set-valued functors) defined on that category.
 It also clarifies how the embedded category, of representable functors and their natural transformations, relates to the other objects in the larger functor category.
 It is an important tool that underlies several modern developments in algebraic geometry and representation theory.
 It is named after Nobuo Yoneda.
Athyrium filix-femina, the lady fern or common lady-fern, is a large, feathery species of fern native throughout most of the temperate Northern Hemisphere, where it is often abundant (one of the more common ferns) in damp, shady woodland environments and is often grown for decoration.
Pot marjoram is a common name for a number of species of "Origanum" used as herbs, including:
In mathematics, more specifically in category theory - internal categories are a generalisation of the notion of small category, and are defined with respect to a fixed ambient category.
 If the ambient category is taken to be the category of sets then one recovers the theory of small categories.
 In general, internal categories consist of a pair of objects in the ambient category - thought of as the 'object of objects' and 'object of morphisms', together with a collection of morphisms in the ambient category satisfying certain identities.
 Group objects, are common examples of internal categories.
Origanum ( )is a genus of herbaceous perennials and subshrubs in the family Lamiaceae, native to Europe, North Africa, and much of temperate Asia, where they are found in open or mountainous habitats.
 A few species also naturalized in scattered locations in North America and other regions.
Athyrium yokoscense, commonly known as Asian common ladyfern in English and as "Hebino-negoza" in Japanese, is a species of fern in the family "Athyriaceae".
 These tough plants live primarily in and around mine sites and thrive in soils contaminated with high concentrations of heavy metals, such as zinc, cadmium, lead, and copper.
 "A. yokoscense" is indigenous to Japan, Korea, eastern Siberia and northeastern China and has been known for centuries to tolerate phytotoxic mining sites.
 The predominance and concentration of this fern species at a particular region was used to identify potential mining sites.
 The primary potential of "A. yokoscense" is in its phytoremediative ability to accumulate toxic metals from soils contaminated with heavy metals, so it may have some long-term commercial importance.
 No medicinal or culinary values of this fern species have been studied or confirmed.
Retusin is an O-methylated flavonol, a type of flavonoid.
 It can be found in "Origanum vulgare" and in "Ariocarpus retusus".