This subtopic studies general category theory, covering foundational notions such as functors, natural transformations, limits, and adjunctions.

This subtopic studies special categories, focusing on classes of categories with additional axioms or structure that support refined constructions.

This subtopic studies categories and algebraic theories, linking categorical language with universal algebra, syntax, and abstract model construction.

This subtopic studies categorical structures, including internal objects, fibrations, and enriched constructions that organize mathematics at a structural level.

This subtopic studies categories in geometry and topology, where categorical methods encode spaces, maps, and invariants in a flexible abstract framework.

This subtopic studies homological algebra, including chain complexes, derived functors, and derived categories used across modern algebra and geometry.

This subtopic studies monoidal and enriched categories, emphasizing tensor-like structures and enriched hom-objects for advanced categorical modeling.

This subtopic studies higher categories, where morphisms between morphisms and multi-level coherence conditions refine categorical foundations.