Difference between revisions of "Product and coproduct compared"
From Maths
(Created page with "__TOC__ ==Overview== The pages product and coproduct pages make it hard to see just how similar the two definiti...") |
m (→Definition) |
||
| Line 31: | Line 31: | ||
|} | |} | ||
| − | We call the arrow {{M|m}} the | + | We call the arrow {{M|m}} ''the mediating arrow''<ref name="AITCTHS2010"/> ({{AKA}}: ''mediator''<ref name="AITCTHS2010"/>) for the [[wedge (category theory)|wedge]] on {{M|X}} |
| + | |||
==Notation== | ==Notation== | ||
The [[product (category theory)|product]] is usually denoted {{M|\times}} and the [[coproduct (category theory)|coproduct]] by {{M|+}}, if they agree (are the same) then we use {{M|\oplus}} | The [[product (category theory)|product]] is usually denoted {{M|\times}} and the [[coproduct (category theory)|coproduct]] by {{M|+}}, if they agree (are the same) then we use {{M|\oplus}} | ||
Latest revision as of 16:59, 1 March 2016
Contents
[hide]Overview
The pages product and coproduct pages make it hard to see just how similar the two definitions are. As a result I shall steal the format from[1] and do a two-column layout showing the differences and similarities.
Definition
Given a pair A, B of objects in a category C a:
| Product | Coproduct |
|---|---|
| is a wedge | |
| with the following universal property; for each wedge: | |
| there exists a unique arrow | |
| X⟶mS | S⟶mX |
| such that the following diagram commutes | |
We call the arrow m the mediating arrow[1] (AKA: mediator[1]) for the wedge on X
Notation
The product is usually denoted × and the coproduct by +, if they agree (are the same) then we use ⊕
(Unknown grade)
This page is a stub
This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:
This notation thing needs expanding
References
- ↑ Jump up to: 1.0 1.1 1.2 An Introduction to Category Theory - Harold Simmons - 1st September 2010 edition
| ||||||||||||||||||||||||||||||||
