Lifting properties and model categories

Related lectures (29)

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

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

Explores natural transformations in algebra, defining functors and isomorphisms.

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

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

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

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

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

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

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