Category Theory For Beginners: Elementary Machinery

In this video we study terminal objects, initial objects, (co)products and (co)equalizers. We prove various results about how these elementary limits and colimits relate to each other and special arrows like monics. For example, we show that equalizers are monics holding the arrows that yield the same result when composed with either of the parallel arrows. For concrete examples, we also explain how monics, terminal objects, initial objects, (co)products and (co)equalizers work in categories of functors into Set. This gives many opportunities to understand how the concepts work in concrete scenarios.

An explicit description of how to construct limits and colimits in functor categories (as well as how to understand exponential objects and subobject classifiers, and also about relations with presheaves), can be found here:

   • Category Theory For Beginners: Preshe...  

A description of how finite limits can be constructed by combining terminal objects, products, and equalizers can be found here:

   • Limits via equalizers 1  

   • Limits via equalizers 2