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Homotopical Algebra: Examples and Adjunctions
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Related lectures (32)
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Introduction to simplicial sets: Simplicial sets
Introduces the category of simplicial sets and explores the standard n-simplex as a universal example.
Forgetful functors vs. properties
Explores forgetful functors, properties, and functor categories through examples and discussions.
Limits and Colimits: Equalizers and Coequalizers
Covers limits and colimits, focusing on equalizers and coequalizers in category theory.
Category Theory: G-sets and Left Adjoint Functor
Explores the construction of G-sets and left adjoint functors in category theory.
Algebraic Kunneth Theorem
Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.
Existence of Left Derived Functors
Explores the existence of left derived functors in homotopical algebra, focusing on isomorphism conditions and natural transformations.
Group Cohomology
Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
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.
Categories and Functors
Covers categories, functors, and presheaf categories, exploring the relationships between objects and morphisms.
Free Abelian Groups: Group Theory
Explores the concept of free abelian groups as an important left adjoint functor.
