Tagged Questions
1
vote
3answers
126 views
Why isn't every coproduct a product (and vice-versa)?
So I know that every coproduct is not a product, so I am misunderstanding some part of the definition of (co)products. Saying that U is a coproduct (the disjoint union of X1 and X2 below) of objects ...
4
votes
1answer
75 views
Products in the category of sets and (left-)total relations
By a total (or left-total) relation I mean a binary relation $R \subseteq X \times Y$ where there is, for each $x \in X$, at least one $y \in Y$ with $(x,y) \in R$. Equivalently stated, I mean ...
0
votes
1answer
138 views
4
votes
2answers
152 views
When equal products imply equal factors?
Under which additional conditions $a\times b = c\times d \Rightarrow a=c\wedge b=d$ (where $\times$ is a categorical product)?
For example, in the case of Cartesian product, for this is enough when ...
1
vote
1answer
61 views
Direct products in subcategories
I have a several categories some of which are subcategories of others. I want to research properties of products in these categories but don't know where to start.
How direct products in a category ...
5
votes
1answer
183 views
Uncountable product in the category of metric spaces.
I need to prove that category $\mathrm{Met}$ of metric spaces and continuous maps doesnt possess uncountable product of non-one point spaces.
Definition. A pair $(X,\{\pi_\nu:\nu\in\Lambda\})$ where ...
