Infinity category theory: Equivalences and Adjunctions

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Infinity Category Theory: Lecture 2

Explores infinity category theory, covering ABB, Kao-cosmos, homotopy, categories, and equivalences.

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

Introduction to Category Theory: Natural Transformations

Introduces natural transformations in category theory through concrete examples from group theory.

Theory: Adjunctions

Introduces adjunctions between categories, emphasizing equivalence and natural transformations.

Schematic Models: Quasi-Categories and ∞-Groupoids

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

Introduction to Category Theory: Adjunctions (Part 1)

Explores the definition of adjunctions and the relationship between functors.

Natural Transformations

Explores natural transformations between functors, emphasizing their composition-preserving properties and significance in category theory.

Functors: Categories, Functors, and Natural Transformations

Introduces functors, including identity and forgetful functors, and explores duality functors.

Adjunction between Simplicial Sets and Enriched Categories

Covers the adjunction between simplicial sets and simplicially enriched categories, including preservation of inclusions and construction of homotopy categories.

Homotopy Coherent Groups and Quasi-Categories

Covers the characterization of trivial Kan fibrations and the importance of homotopy coherent groups.