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Introduction to simplicial sets: Simplicial sets
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Related lectures (32)
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Simplicial and Cosimplicial Objects: Examples and Applications
Covers simplicial and cosimplicial objects in category theory with practical examples.
Natural Transformations in Algebra
Explores natural transformations in algebra, defining functors and isomorphisms.
Limits and colimits as adjoints: Chapter 1(c)
Explores the characterization of limits and colimits as adjoints in category theory.
Homotopical Algebra: Functor and Adjunctions
Delves into homotopical algebra, defining functors and adjunctions with examples.
Active Learning Session
Explores natural transformations in group theory and category theory, emphasizing functor composition and morphism composition.
Construction of the homotopy category
Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.
From Simplicial Categories to Quasicategories
Introduces the construction of quasi-categories from Kan enriched categories through defining simplicially enriched categories and constructing the simplicial nerve functor.
Active Learning: Functors and Geometric Realization
Covers the computation of nerves and geometric realization in simplicial sets, along with functors into and out of the category of simplicial sets.
Homotopical Algebra
Covers the theory of groups and homotopical algebra, emphasizing natural transformations, identities, and isomorphism of categories.
Functor Categories: (Co)Limits and Simplicial Sets
Explores (co)limits in functor categories and simplicial sets, including equalizers and coequalizers of simplicial maps.