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Concept

Nerve (category theory)

Related lectures (32)

Delves into the computation and geometric realization of small categories, exploring the relationship between nerves and geometric structures.

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

Introduces the category of simplicial sets and explores the standard n-simplex as a universal example.

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

Covers the computation of nerves and geometric realization in simplicial sets, along with functors into and out of the category of simplicial sets.

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

Explores the homotopy theory of chain complexes, including path object construction and fibrations.

Explores the characterization of limits and colimits as adjoints in category theory.

Covers the study of lifting properties in categories, focusing on the left and right lifting properties.

Explores the restriction functor in group theory, focusing on its properties.

Delves into direct sums of abelian groups, showcasing their coproduct properties and universal verification.

Introduces natural transformations in group theory and category theory, emphasizing their definition and significance.

Introduces two fundamental examples of simplicial sets: the nerve of a small category and the singular simplicial set of a topological space.

Covers the definition and properties of natural transformations between functors in category theory.

Introduces limits and colimits in a category, covering their properties and uniqueness.

Introduces functors in category theory and explains their composition.

Explores right extensions in infinity category theory and their equivalent definitions.

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

Covers natural transformations, functors, and their composition properties in category theory.

Explores the epsilon transformation in group theory and category theory, emphasizing linearity and naturality.