The relation-algebra tag has no wiki summary.

**1**

vote

**0**answers

64 views

### The relation on the set of functions

Let $\varphi: \mathbb{R}^{2} \to \mathbb{R}$ be a symmetric (not necessarily continuous) function (so, $\varphi(x,y)=\varphi(y,x)$ $\forall (x,y)\in \mathbb{R}^{2}$),
let $\mathcal{F}$ be the set of ...

**2**

votes

**2**answers

356 views

### Categories with binary relations as objects

For the category of functions, pairs of functions making commutative diagrams are the canonical morphisms $\alpha:f\rightarrow g$. For binary relations there is an alternative, to consider the ...

**0**

votes

**0**answers

109 views

### Name of Property $t=st \text{ and } s=ts$

What is the name of the property shared by a pair of functions $s,t$ with $$t=st \text{ and } s=ts$$
( Main example: relation-valued domain and range operations on relations, via ...

**50**

votes

**11**answers

3k views

### Why is Set, and not Rel, so ubiquitous in mathematics?

The concept of relation in the history of mathematics, either consciously or not, has always been important: think of order relations or equivalence relations.
Why was there the necessity of singling ...

**2**

votes

**1**answer

202 views

### Why is a UNION operation independent in relational algebra?

Why is a set union operation independent in relational algebra? Why it cannot by expressed by the other four basic operations (selection, projection, cartesian product and difference)? What kind of ...

**1**

vote

**0**answers

121 views

### Substitution semiring?

Let G be a [ CF ] grammar, and let elements of semiring be sets of rules.
Define multiplication as:
$$ x\otimes y = \{ t| \exists r \in x \exists s \in y (t=subst(r,s))\} $$
where $subst(r,s)$ ...

**1**

vote

**2**answers

374 views

### Calculus of Binary Relations

I was reading "Origins of the Calculus of Binary Relations" by Vaughan Pratt where he says "it consists of two components, a logical or static component and a relative or dynamic component" but it ...