rmehta wrote a new post, (Co)homology and Exactness, on the site My deep dive into Algebraic Geometry 4 days, 8 hours ago
$newcommand{im}{text{im}}newcommand{ker}{text{ker}}newcommand{cok}{text{coker}}newcommand{coim}{text{coim}}$In this post, we’ll generalize the notions of homology, cohomology, and exactness from […]
rmehta wrote a new post, Abelian Categories, on the site My deep dive into Algebraic Geometry 2 weeks, 2 days ago
$newcommand{Mor}{operatorname{Mor}}newcommand{Hom}{operatorname{Hom}}newcommand{id}{operatorname{id}}newcommand{im}{operatorname{im}}newcommand{cok}{operatorname{coker}}$If you’ve survived the drawl […]
rmehta wrote a new post, Yoneda Lemma, on the site My deep dive into Algebraic Geometry 2 weeks, 3 days ago
$newcommand{Mor}{operatorname{Mor}}newcommand{id}{operatorname{id}}$Before we move on to the more involved structures in Category Theory, it’s worth taking a detour through proving Yoneda’s lemma. Roughly […]
rmehta wrote a new post, Universal Properties, on the site My deep dive into Algebraic Geometry 2 weeks, 5 days ago
$newcommand{Mor}{operatorname{Mor}}newcommand{id}{operatorname{id}}$As mentioned in *Why bother with Category Theory?*, universal properties are part of the key appeal of category theory, since they are easy […]
rmehta commented on the post, Universal Properties, on the site My deep dive into Algebraic Geometry 2 weeks, 5 days ago
For some reason, this post is bugged, and the last few bullets aren’t rendering correctly, so I’m going to make a new post with examples of adjoints and other universal properties.
rmehta wrote a new post, Examples of basic categories and tools, on the site My deep dive into Algebraic Geometry 2 weeks, 6 days ago
## Category examples$newcommand{Mor}{operatorname{Mor}}newcommand{id}{operatorname{id}}$
– The collection of all sets, with $Mor(A,B)$ being the set of all functions $Ato B$, and $id_A(x)=x$ for all […]rmehta wrote a new post, Why bother with Categories?, on the site My deep dive into Algebraic Geometry 2 weeks, 6 days ago
$newcommand{Mor}{operatorname{Mor}}newcommand{id}{operatorname{id}}$The definition of a category seems somewhat uninspired when you first encounter it. What are “objects”? What are “morphisms”? Why bother […]
rmehta wrote a new post, What is a category?, on the site My deep dive into Algebraic Geometry 1 month ago
$newcommand{Mor}{operatorname{Mor}}newcommand{id}{operatorname{id}}$A **category** is a collection of *objects*, and for any two objects $A,B$, a collection of *morphisms* between them. For a category […]
rmehta wrote a new post, Introduction, on the site My deep dive into Algebraic Geometry 1 month ago
To any readers, hello!
The purpose of this blog is two-fold: to document my process of learning algebraic geometry, and to hold myself accountable to keep learning while life pulls me in other ways.
I’ll be […]
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