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Invariant Definitions
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Related lectures (39)
Limits and colimits in Top
Covers the concepts of limits and colimits in the category of Topological Spaces, emphasizing the relationship between colimit and limit constructions and adjunctions.
Simplicial and Cosimplicial Objects: Examples and Applications
Covers simplicial and cosimplicial objects in category theory with practical examples.
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
Covers categories, functors, and presheaf categories, exploring the relationships between objects and morphisms.
Adjunctions and Limits: Exploring Functors and Co-limits
Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.
Endomorphisms and automorphisms of totally disconnected locally compact groups I
Covers the definitions and basic results of endomorphisms and automorphisms of totally disconnected locally compact groups.
Concrete Categories
Covers concrete categories with sets and structures, including Ens, Gr, Ab, and Vectk.
Sets and Operations: Introduction to Mathematics
Covers the basics of sets and operations in mathematics, from set properties to advanced operations.
Endomorphisms and automorphisms of totally disconnected locally compact groups II
Explores flat groups of automorphisms and their properties, including minimization functions and invariance under specific conditions.
Functions: Definitions and Notations
Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.
Functors and Adjunctions
Explores functors between categories and the conditions for left and right adjoints.
Cartesian Product and Induction
Introduces Cartesian product and induction for proofs using integers and sets.
Adjunctions: Constructing Desired Adjoints
Explores constructing desired adjoints in specific categories like Set.
Group Actions: G-objects in a Concrete Category
Explores G-objects in a concrete category and the framework for group actions.
Group Theory: Basics
Covers the basics of group theory, including sets, applications, and examples like permutations and rotations.
Categories and Functors
Explores building categories from graphs and the encoding of information by functors.
Mapping Functions and Surjections
Explores mapping functions, surjections, injective and surjective functions, and bijective functions.
Existence in Abelian Case and Group Center
Explores the existence of p-Sylow subgroups in finite groups and the abelian group center.
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Free Abelian Groups: Group Theory
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Explores the concept of free abelian groups as an important left adjoint functor.
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