Limits and Colimits

Limits and colimits are concepts from category theory that describe how different objects and their relationships unify or combine. Think of a limit as a universal way to gather information from related objects to find a common, most-structured point—like finding a best shared feature among data sets. A colimit, conversely, aggregates multiple objects into a single, unified object—similar to merging several sources into one comprehensive report. These constructions help mathematicians and computer scientists understand how structures relate, combine, or approximate each other within complex systems.