Given a category, the isomorphism class of one of its objects is its equivalence class under the equivalence relation which regards two objects as related when they are connected by an isomorphism.
The set of isomorphism classes of a category is also sometimes thought of as the category’s decategorification.
The isomorphism class of a finite set is a natural number.
The isomorphism class of a set is its cardinality.
The isomorphism class of a vector space is (labeled by) its dimension.
The isomorphism classes of an action groupoid are the orbits of the group action.
Last revised on May 20, 2022 at 13:35:01. See the history of this page for a list of all contributions to it.