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Limits and colimits: Two examples
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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: 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.
Categories and Functors: An Introduction
Provides an overview of categories, functors, and natural transformations in mathematics.
Simplicial and Cosimplicial Objects: Examples and Applications
Covers simplicial and cosimplicial objects in category theory with practical examples.
Active Learning in Category Theory
Explores examples of categories, morphisms, groupoids, and functors in category theory.
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Covers morphisms with lifting properties, pushouts, pullbacks, and the uniqueness in the universal property of pushouts.
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Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.
Introduction to Coproducts
Introduces coproducts in category theory, exploring their properties, universality, and relationships with products.
Introduction to Categories: Products and Coproducts
Introduces the theory of categories by generalizing the Cartesian product and disjoint union of sets to any category.
Products: Theory of Categories
Covers the concept of products in category theory, focusing on their properties, uniqueness, and isomorphisms.
