Preadditive category

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Quasicategories: An Alternative Homotopy Theory

Introduces quasicategories as an alternative approach to defining homotopy maps and categories.

Active Learning in Category Theory

Explores examples of categories, morphisms, groupoids, and functors in category theory.

Group representations constructions

Explores the construction of group representations through various methods and provides an illustrative example using the standard representation of sr2 on c2.

Schematic Models: Quasi-Categories and ∞-Groupoids

Covers schematic models, emphasizing quasi-categories and ∞-groupoids in modeling categories.

Functors: Examples

Explores identity and forgetful functors in category theory, showcasing their role in preserving structure and relationships between categories.

Group Theory Fundamentals

Introduces the basics of group theory, defining groups, categories, and groupoids.

Derived Functors

Explores derived functors, Ext-modules, Yoneda extensions, and derived categories in the context of extending modules.

Active Learning Session: Group Theory

Explores active learning in Group Theory, focusing on products, coproducts, adjunctions, and natural transformations.

Speculative Query Execution: Bottlenecks and Dependencies

Explores speculative query execution for complex queries, addressing bottlenecks, dependencies, and performance prediction.

Limits and Colimits: Understanding Categories

Explores limits and colimits in category theory, discussing their definitions, properties, and applications, including the non-existence of limits in certain categories and the relationships between limits and colimits under functors.