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Lecture
From Simplicial Categories to Quasicategories
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Related lectures (34)
Simplicial and Cosimplicial Objects: Examples and Applications
Covers simplicial and cosimplicial objects in category theory with practical examples.
Limits and colimits as adjoints: Chapter 1(c)
Explores the characterization of limits and colimits as adjoints in category theory.
Transfer of Model Structures
Covers the transfer of model structures through adjunctions in the context of model categories.
Introduction to simplicial sets: Simplicial sets
Introduces the category of simplicial sets and explores the standard n-simplex as a universal example.
Adjunctions and Limits: Exploring Functors and Co-limits
Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.
Adjunctions and Functor Categories: Exploring Connections
Covers adjunctions and functor categories, emphasizing their significance in category theory and applications in deep learning.
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.
Limits and colimits: Introduction, Chapter 1(c)
Introduces limits and colimits in a category, covering their properties and uniqueness.
Limits and Colimits in Functor Categories
Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.
Categories and Functors: An Introduction
Provides an overview of categories, functors, and natural transformations in mathematics.
Natural Transformations: Examples
Introduces natural transformations through examples, covering equivalence of categories and functor properties.
Functor Categories Composition and Induced Functors
Explores composition of functors, induced functors, and preservation of commutative diagrams in category theory.
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.
Functors and Adjunctions
Explores functors between categories and the conditions for left and right adjoints.
Categories and Functors
Explores building categories from graphs and the encoding of information by functors.
Natural Transformations in Group Theory
Introduces natural transformations in group theory and category theory, emphasizing their definition and significance.
Natural Transformations: Definition
Covers the definition and properties of natural transformations between functors in category theory.
Functors: Definition
Introduces functors in category theory and explains their composition.
Natural Transformations
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Explores natural transformations between functors, emphasizing their composition-preserving properties and significance in category theory.
Natural Transformations: Examples and Applications
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Explores natural transformations between functors in different categories and their applications.
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