Pointed category: why is it defined that way?

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. … Continue reading Pointed category: why is it defined that way?

Homeomorphism is not just continuous bijection

A common mistake people make is to think that a continuous bijection is a homeomorphism. This is a reasonable mistake. A bijection is an isomorphism of sets.  A bijective homomorphism of groups is an isomorphism of groups. In most algebraic settings I can think of this pattern holds. But it is not true of topological … Continue reading Homeomorphism is not just continuous bijection