- Introductory Category Theory Notes - UC Santa Barbara
The Yoneda Lemma is a canonical embedding of a locally small category C into the category [Cop; Set], generally known as the category of presheaves on C, PSh(C)
- Introducing Category Theory - Logic Matters
Category theory provides a basic tool-kit, and it throws very revealing light on ideas which recur across mathematics This book is a based on a much-downloaded set of notes, and aims to give a gentle introduction to some core categorial concepts
- Category Theory - Auburn University
Category theory shifts the focus away from the elements of the objects and toward the morphisms between the objects In fact, the axioms of a category do not require that the objects actually be sets, so that in general it does not even make sense to speak of the elements of an object
- Category Theory - Cornell University
Category theory has been around for about half a century now, invented in the 1940’s by Eilenberg and MacLane Eilenberg was an algebraic topologist and MacLane was an algebraist
- Category theory in context Emily Riehl
ructure-preserving morphisms is clear However, this practice is somewhat contrary to the basic philosophy of category theory: that mathematical objects should always be considered in andem with the morphisms between them As we have seen, the category can be recovered from the algebra of morphisms so of the two, the objects and morphisms, the
- 18. S996S13 Textbook: Basic category theory - MIT OpenCourseWare
In everyday speech we think of a category as a kind of thing A category consists of a collection of things, all of which are related in some way In mathematics, a category can also be construed as a collection of things and a type of relationship between pairs of such things
- Tutorial topic: Category Theory - Harvard University
This tutorial will introduce the tools of category theory, focusing on examples tailored to participants' back-grounds Fundamental concepts such as categories, functors, natural transformations, representability, limits and colimits, and adjunctions will be covered in detail
|