Homotopy Type Theory

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Related lectures (31)

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Homotopy Theory in Chain Complexes

Explores acyclic fibrations and cylinder objects in chain complexes.

Homotopy Theory of Chain Complexes

Explores the model structure on chain complexes over a field.

Elementary Properties of Model Categories

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

Cylinder Construction on Chain Complex

Explores the cylinder construction on a chain complex and its equivalence to chain homotopy.

Retracte: Fundamental Group and Cell Attachment

Covers the concept of a subspace being a retract of another space and fundamental groups, including examples like contracting the teeth of a necklace.

Homotopy and Quotient Spaces

Covers homotopy, quotient spaces, and the universal property in topology.

Chain Homotopy and Projective Complexes

Explores chain homotopy, projective complexes, and homotopy equivalences in chain complexes.

Homotopy Equivalence in Chain Complexes

Explores homotopy equivalence in chain complexes, emphasizing path object construction and left/right homotopy characterization.

Quotient Spaces: Three Ways

Explores three ways to form quotient spaces using group actions and equivalence relations.

Homotopy Theory in Care Complexes

Explores the construction of cylinder objects in chain complexes over a field, focusing on left homotopy and interval chain complexes.