Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Higher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities. N-categories are defined inductively using the enriched category theory: 0-categories are sets, and (n+1)-categories are categories enriched over the monoidal category of n-categories (with the monoidal structure given by finite products). This construction is well defined, as shown in the article on n-categories. This concept introduces higher arrows, higher compositions and higher identities, which must well behave together. For example, the category of small categories is in fact a 2-category, with natural transformations as second degree arrows. However this concept is too strict for some purposes (for example, homotopy theory), where "weak" structures arise in the form of higher categories.

Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.