Lectures related to Lifting properties and model categories

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

Lifting Properties in Model Categories: An Overview

Provides an overview of lifting properties in model categories, focusing on their definitions and implications for morphisms and commutative diagrams.

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.

Adjunctions and Limits: Exploring Functors and Co-limits

Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.

Transfer of Model Structures

Covers the transfer of model structures through adjunctions in the context of model categories.

Limits and Colimits in Functor Categories

Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.

Introduction to Model Categories

Explores lifting properties and model categories in topological spaces.

Homotopy Theory of Chain Complexes

Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.

Homotopy theory of chain complexes

Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.

Active Learning Session: Group Theory

Explores active learning in Group Theory, focusing on products, coproducts, adjunctions, and natural transformations.

Homotopy Theory: Cylinders and Path Objects

Covers cylinders, path objects, and homotopy in model categories.

Homotopy Categories: Model Structures

Explores homotopy categories in model structures, emphasizing weak equivalences and the Whitehead Lemma.

Natural Transformations in Algebra

Explores natural transformations in algebra, defining functors and isomorphisms.

Categories and Functors

Explores building categories from graphs and the encoding of information by functors.

Limits and colimits: Two examples

Focuses on the pushout and pullback constructions in sets, illustrating colimits and limits with explicit examples.

Homotopy Coherent Groups and Quasi-Categories

Covers the characterization of trivial Kan fibrations and the importance of homotopy coherent groups.

Quillen Equivalences

Explores Quillen equivalences, emphasizing the preservation of cofibrations and acyclic cofibrations.

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Categories and Functors

Covers categories, functors, and presheaf categories, exploring the relationships between objects and morphisms.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.