Lectures related to Derived category

Derived functors: Identity and Homotopy Categories

Explores derived functors in model categories, focusing on identity and homotopy categories.

Derivability on an Interval: Rolle's Theorem

Covers derivability on an interval, including Rolle's Theorem and practical applications in function analysis.

Derivability and Composition

Covers derivability, linear applications, composition of functions, and the gradient vector.

Tangent to Graph of a Function

Explores finding the equation of the tangent line to a function's graph at a point.

Derivatives and Limits: Generalization and Indeterminacy

Covers the generalization of the TAF theorem, lateral derivatives, limits of derivatives, and indeterminacy.

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.

Differential Calculus: Definition and Derivability

Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.

Homotopy Coherent Groups and Quasi-Categories

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

Fields Deriving from a Potential

Explores fields deriving from a potential, emphasizing integral and linear aspects.

Linear Approximation and Derivative Parametric

Covers linear approximation, parametric derivatives, and differentiability conditions on intervals.

Group Cohomology

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Adjunction between Simplicial Sets and Enriched Categories

Covers the adjunction between simplicial sets and simplicially enriched categories, including preservation of inclusions and construction of homotopy categories.

Derivability and Continuity

Explores continuity, derivability, and linear approximation in mathematical analysis.

Continuity and Derivability in Heat Analysis

Explores continuity and derivability in heat analysis, emphasizing uniform convergence and mathematical proofs.

Derivability and Composition

Covers derivability conditions, function composition, Jacobian matrix, and chain derivation.

Analyse I: Derivatives and Continuity

Explores the consequences of derivatives and the constancy of functions.

Introduction to Category Theory: Natural Transformations

Introduces natural transformations in category theory through concrete examples from group theory.

Adjunctions and Limits: Exploring Functors and Co-limits

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

Cohomology: Recollection and Foliations

Covers cohomology, injective resolutions, and acyclic objects in an abelian category.

Homotopy Category and Derived Functors

Explores the homotopy category of chain complexes and the relation between quasi-isomorphisms and chain homotopy equivalences.