Concept

Direct limit

Related lectures (20)

Covers the concepts of limits and colimits in the category of Topological Spaces, emphasizing the relationship between colimit and limit constructions and adjunctions.

Sheaves: Hartshorne I.1

Covers the concept of sheaves, emphasizing the unique determination of functions by local data and the importance of direct limits.

Homotopy Theory of Chain Complexes

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

Inverse Limits and Topologies

Explores inverse limits, profinite completions, and Hausdorff topologies in group theory and topology.

Limits and Colimits in Functor Categories

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

Adjunctions and Limits: Exploring Functors and Co-limits

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

Multicorrelation Sequences and Primes

Explores multicorrelation sequences, primes, and their intricate connections in number theory and ergodic theory.

Homotopy Identification

Delves into homotopy identification, pushout diagrams, colimits, and group fundamental calculations.

Vector Calculus: 3D Orientation and Cross Product

Covers 3D orientation, cross product, and volume calculations using mixed product in vector calculus.

Two Propositions

Discusses two propositions about converging sequences of real numbers and explores their consequences.

Limit of a Function

Covers the discussion of real functions and the concept of limits.

Bisection Algorithm: Convergence and Continuity

Explores the Bisection Algorithm, convergence of sequences, and function continuity.

Subsequences and Bolzano-Weierstrass Theorem

Covers the proof of the Squeeze Theorem, Quotient Criteria, and the Bolzano-Weierstrass Theorem.

Operations on Limits

Explores algebraic operations on limits of sequences and discusses the uniqueness of limits and properties of convergent and divergent sequences.

Convergence and Limits in Real Numbers

Explains convergence, limits, bounded sequences, and the Bolzano-Weierstrass theorem in real numbers.

Sequence Convergence: Definitions and Properties

Covers definitions and properties of sequence convergence, including limits, uniqueness, and the two gendarmes theorem.

Limits and colimits: Introduction, Chapter 1(c)

Introduces limits and colimits in a category, covering their properties and uniqueness.

Response Theory and Phase Transitions

Explores response theory, phase transitions, and fluctuations in weakly interacting systems, including stochastic particles and opinion formation models.

Continuity of Trigonometric Functions

Explores the continuity of trigonometric functions and demonstrates specific limits and propositions related to them.

Limits and colimits: Two examples

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