Homotopical connectivity

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Related lectures (32)

Homotopical Algebra: Functor and Adjunctions

Delves into homotopical algebra, defining functors and adjunctions with examples.

Derived Functors in Homotopical Algebra

Covers the Fundamental Theorem of homotopical algebra, Quillen pairs, and derived functors.

Homotopical Algebra

Covers the theory of groups and homotopical algebra, emphasizing natural transformations, identities, and isomorphism of categories.

Homotopical Algebra: Theory and Applications

Explores homotopical algebra, covering colimits, limits, adjunctions, and their applications in group theory.

Homotopical Algebra: Examples and Adjunctions

Explores homotopical algebra examples and adjunctions, focusing on left and right adjoints in group functors and coproducts.

Symmetries and Groups in Quantum Mechanics

Covers the role of symmetries and groups in quantum mechanics, focusing on SU2 and SU3, their properties, and implications for physical theories.

Homotopical Algebra: (Co)Limits

Explores the concept of (co)limits in homotopical algebra, discussing functor relations, special cases, and the universal properties of colimits and limits.

Derived functors: Two technical lemmas

Covers two technical lemmas essential for the Fundamental Theorem in homotopical algebra.

Existence of Left Derived Functors

Explores the existence of left derived functors in homotopical algebra, focusing on isomorphism conditions and natural transformations.

Existence of Left Derived Functors: Part 2

Concludes the proof of the existence of left derived functors and discusses total left and right derived functors.

Elementary Properties of Model Categories

Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.

Natural Transformations in Algebra

Explores natural transformations in algebra, defining functors and isomorphisms.

Left Homotopy as an Equivalence Relation: The Homotopy Relation in a Model Category

Explores the left homotopy relation as an equivalence relation in model categories.

Homotopy Theory: Cylinders and Path Objects

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

Homology of Riemann Surfaces

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.

The Whitehead Lemma: Homotopy Equivalence in Model Categories

Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.

Introduction to Derived Functors: Left and Right Derived Functors

Introduces left and right derived functors in homotopical algebra, emphasizing their uniqueness and providing an illustrative example.

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Construction of the homotopy category

Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.

Relative Homotopy Groups

Covers relative homotopy groups, establishing long exact sequences and defining boundary homomorphisms.

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