From Simplicial Categories to Quasicategories

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Related lectures (34)

Limits and Colimits: Understanding Categories Log in to Mediaspace to watch this video

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.

Introduction to Category Theory: Natural Transformations Log in to Mediaspace to watch this video

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

Model Categories and Homotopy Theory: Functorial Connections Log in to Mediaspace to watch this video

Covers the relationship between model categories and homotopy categories through functors preserving structural properties.

Natural Transformations in Algebra Log in to Mediaspace to watch this video

Explores natural transformations in algebra, defining functors and isomorphisms.

Introduction to Category Theory: Adjunctions (Part 1)Log in to Mediaspace to watch this video

Explores the definition of adjunctions and the relationship between functors.

Active Learning Session Log in to Mediaspace to watch this video

Explores natural transformations in group theory and category theory, emphasizing functor composition and morphism composition.

Introduction to Category Theory: Natural Transformations Log in to Mediaspace to watch this video

Covers the concept of natural transformations between functors and their associativity.

Active Learning in Category Theory Log in to Mediaspace to watch this video

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

Group Actions and Functors Log in to Mediaspace to watch this video

Covers group quotient, group actions, and functors connecting sets and G-sets.

Natural Learning Session Log in to Mediaspace to watch this video

Explores coproducts, universal properties, and natural transformations in category theory.

Equivalences of Categories Log in to Mediaspace to watch this video

Explores examples of natural transformations, equivalence of categories, and adjunction with specific instances involving Un.

Free Abelian Groups: Group Theory Log in to Mediaspace to watch this video

Explores the concept of free abelian groups as an important left adjoint functor.

Group Theory: Adjoint Functors and G-sets Log in to Mediaspace to watch this video

Explores adjunction between functors, composition of applications, G-equivariance, and natural transformations in G-sets.

Singular Homology: First Properties Log in to Mediaspace to watch this video

Covers the first properties of singular homology and the preservation of decomposition and path-connected components in topological spaces.

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