/explore
|
You are here 
|
bartoszmilewski.com | ||
| | | | |
bmbumpus.com
|
|
| | | | | In a previous post, we discussed sieves, the sieve-y definition of Grothendieck topologies and a few exaples thereof. Today we'll return to sheaves, but this time we do so armed with a better understanding of sites (the "places" in which to define sheaves). This post consists of notes and reflections from reading Daniel Rosiak's book | |
| | | | |
dominiczypen.wordpress.com
|
|
| | | | | The starting point of this blog post is a slight reformulation of the $latex T_0$ separation axiom: A topological space $latex (X,\tau)$ is $latex T_0$ if for all $latex x\neq y\in X$ there is a set $latex U\in \tau$ such that $latex \{x,y\}\cap U \neq \emptyset \text{ and } \{x,y\}\not\subseteq U.$ Given a cardinal $latex... | |
| | | | |
www.jeremykun.com
|
|
| | | | | Last time we worked through some basic examples of universal properties, specifically singling out quotients, products, and coproducts. There are many many more universal properties that we will mention as we encounter them, but there is one crucial topic in category theory that we have only hinted at: functoriality. As we've repeatedly stressed, the meat of category theory is in the morphisms. One natural question one might ask is, what notion of morphism is there between categories themselves? | |
| | | | |
bluebirdofbitterness.com
|
|
| | | Reblogged on WordPress.com | ||
