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.
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.
Pimelea (often seen spelled "Pimelia", which is the name of a genus of beetles) is a genus of plants belonging to the family Thymelaeaceae.
 There are about 80 species in the genus, which is native to Australia and New Zealand.
 Many of the species are poisonous to cattle and horses.
A dagger symmetric monoidal category is a monoidal category formula_1 which also possesses a dagger structure; in other words, it means that this category comes equipped not only with a tensor in the category theoretic sense but also with dagger structure which is used to describe unitary morphism and self-adjoint morphisms in formula_2 that is, a form of abstract analogues of those found in FdHilb, the category of finite-dimensional Hilbert spaces.
 This type of category was introduced by Selinger as an intermediate structure between dagger categories and the dagger compact categories that are used in categorical quantum mechanics, an area which now also considers dagger symmetric monoidal categories when dealing with infinite-dimensional quantum mechanical concepts.
Hurricane Hugo was a powerful Cape Verde–type hurricane that caused widespread damage and loss of life in the Leeward Islands, Puerto Rico, and the Southeast United States.
 It formed over the eastern Atlantic near the Cape Verde Islands on September 9, 1989.
 Hugo moved thousands of miles across the Atlantic, rapidly strengthening to briefly attain category 5 hurricane strength on its journey.
 It later crossed over Guadeloupe and St. Croix on September 17 and 18 as a category 4 hurricane.
 Weakening slightly more, it passed over Puerto Rico as a strong category 3 hurricane.
 Further weakening occurred several hours after re-emerging into the Atlantic, becoming downgraded to a category 2 hurricane.
 However, it re-strengthened into a category 4 hurricane before making landfall just slightly north of Charleston, on Isle of Palms on September 21 with 140 mph sustained winds (gusts to more than 160 mph).
 It had devolved to a remnant low near Lake Erie by the next day.
 As of 2016, Hurricane Hugo is the most intense tropical cyclone to strike the East Coast north of Florida since 1900.
Disocactus is a genus of epiphytic cacti in the tribe Hylocereeae found in Central America, the Caribbean and northern South America.
 It should not be confused with "Discocactus", which is a different genus.
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 .
The plants known as epiphyllum hybrids, epiphyllums, epicacti or just epis, widely grown for their flowers, are artificial hybrids of species within the group of cacti placed in the tribe Hylocereeae, particularly species of "Disocactus", "Pseudorhipsalis" and "Selenicereus".
 In spite of the common name, species in the genus "Epiphyllum" are less often involved as parents of epiphyllum hybrids.
Pimelea humilis, also known as common riceflower or dwarf riceflower, is a shrub in the family Thymelaeaceae, native to Australia.
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.

Question: What type of category does Pimelea and Disocactus have in common?
Answer: genus