Category Archives: Category Theory

Sometimes the ideas of (co)limits and subcategories don’t really play nicely with each other. A (co)limit of a diagram in a category has two basic pieces. One is an object of the category which people usually think of as being the “result” of taking the (co)limit. The other is a (co)cone, which is a bunchContinueContinue reading “(Co)products and Subcategories”

Before I start talking about what I want, I should point out that pointed category is pretty much the lowest generalization of abelian category, which is an important concept when thinking about algebra from a categorical perspective. What is a pointed category? What should the term ‘pointed category’ refer to? Let’s start with a simpler case.ContinueContinue reading “Pointed category: why is it defined that way?”

By “categorical network theory”, I mean the study of networks or graphs using category theory. A lot of the time, the graphs in these works are morphisms in a category, or 1-cells in some sort of 2-dimensional category. Here are some papers on categorical network theory: 2013 Spivak, The operad of wiring diagrams: formalizing aContinueContinue reading “Reference List: Categorical Network Theory”