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Homotopical Algebra: Theory and Applications
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Related lectures (32)
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Limits and Colimits: Understanding Categories
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.
Limits and colimits: Introduction, Chapter 1(c)
Introduces limits and colimits in a category, covering their properties and uniqueness.
Algebraic Kunneth Theorem
Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.
Adjunctions and (co)limits: Limits and colimits
Explores how adjunctions relate to limits and colimits, proving their preservation properties.
Active Learning: Group Theory
Explores adjoint functors, points fixes, orbits, and non-trivial actions in group theory.
Equivalences of Categories
Explores examples of natural transformations, equivalence of categories, and adjunction with specific instances involving Un.
Group Actions and Functors
Covers group quotient, group actions, and functors connecting sets and G-sets.
Existence of Left Derived Functors
Explores the existence of left derived functors in homotopical algebra, focusing on isomorphism conditions and natural transformations.
Introduction to Category Theory: Functors
Covers the concept of functors in category theory, including composition, identity functors, and forgotten functors.
Acyclic Models: Cup Product and Cohomology
Covers the cup product on cohomology, acyclic models, and the universal coefficient theorem.
