Search results
Results from the WOW.Com Content Network
Even if the shapes, sizes, and objects are radically different, they will appear as a group if they are close. Refers to the way smaller elements are "assembled" in a composition. Also called "grouping", the principle concerns the effect generated when the collective presence of the set of elements becomes more meaningful than their presence as ...
Categorization is a type of cognition involving conceptual differentiation between characteristics of conscious experience, such as objects, events, or ideas.It involves the abstraction and differentiation of aspects of experience by sorting and distinguishing between groupings, through classification or typification [1] [2] on the basis of traits, features, similarities or other criteria that ...
An algebraic group is a group object in the category of algebraic varieties. In modern algebraic geometry, one considers the more general group schemes, group objects in the category of schemes. A localic group is a group object in the category of locales. The group objects in the category of groups (or monoids) are the abelian groups.
Geometric group theory attacks these problems from a geometric viewpoint, either by viewing groups as geometric objects, or by finding suitable geometric objects a group acts on. [7] The first idea is made precise by means of the Cayley graph, whose vertices correspond to group elements and edges correspond to right multiplication in the group.
In mathematics, particularly category theory, a 2-group is a groupoid with a way to multiply objects, making it resemble a group. They are part of a larger hierarchy of n-groups. They were introduced by Hoàng Xuân Sính in the late 1960s under the name gr-categories, [1] [2] and they are also known as categorical groups.
A crude sense of cardinality, an awareness that groups of things or events compare with other groups by containing more, fewer, or the same number of instances, is observed in a variety of present-day animal species, suggesting an origin millions of years ago. [4]
Categories include sets, groups and topologies. Each category is distinguished by properties that all its objects have in common, such as the empty set or the product of two topologies, yet in the definition of a category, objects are considered atomic, i.e., we do not know whether an object A is a set, a topology, or any other abstract concept ...
When combined in different relations to each other (e.g., on-top-of, larger-than, end-to-end, end-to-middle) and coarse metric variation such as aspect ratio and 2D orientation, billions of possible 2- and 3-geon objects can be generated. Two classes of shape-based visual identification that are not done through geon representations, are those ...