0
votes
0answers
38 views

What do we call those functions that can be obtained from term operations by partial evaluation?

Let $T$ denote an algebraic theory and suppose $X$ is a $T$-algebra. Then a term operation of $X$ is a function $f : X^n \rightarrow X$ that is definable by an expression in the language of $T$. ...
2
votes
1answer
36 views

Is there a phrase to describe those objects of $\mathbf{C}$ that can be expressed as quotients of the algebra freely generated by $X$?

Let $\mathbf{C}$ denote the category of models of an algebraic theory in $\mathbf{Set}.$ Now suppose $X$ is an object of $\mathbf{Set}$. Is there a traditional phrase used to describe those objects of ...
0
votes
0answers
24 views

Terminology in universal algbera

(Fix throughout a functional language $\Sigma$.) Given an algebra $A$ with underlying set $\vert A\vert$, there is an obvious surjective homomorphism from $A$ to the free algebra generated by $\vert ...
0
votes
0answers
60 views

What do we call functions that are definable by expressions?

Let $X$ denote a model of an algebraic theory $T$. What do we call the functions $f : X^n \rightarrow X$ that are definable by some expression in the language of $T$? e.g. If $S_3$ is the symmetric ...
0
votes
0answers
142 views

Collections of Homomorphic (defined) structures via $f$

Long ago I read a text about a collection of algebraic sturctures all homomorphic (or isomorphic) via a unique homomorphism An Example similar to the construction I found was this: Lets take define ...
5
votes
0answers
46 views

Is there a name for the algebra of substructures?

Let $X$ denote an entropic algebra (see here), which just means that all the operations of $X$ are homomorphisms $X^n \rightarrow X.$ Abelian groups are the classic example. Then for any operation of ...
0
votes
1answer
54 views

Is there a standard name for a set equipped only with an idempotent binary operation?

Is there a name for an idempotent magma, or do they not arise often enough to warrant a special name? (By idempotent binary operation, I mean an operation $+$ such that $x + x = x$ for any $x$.)
3
votes
1answer
82 views

Completing a Partially Defined Associative Binary Operation

This is more like a question about terminology. I would like to hear some recommendations of books that discuss algebraic structures with one partially defined associative binary operation, and the ...
1
vote
2answers
55 views

Notation for “incommensurate” elements?

Say that $x\wedge y\not=x,y$, that is neither $x\leq y$ nor $y\leq x$. Is there a way to denote this? I've been saying $x<>y$ but that's completely made up.
3
votes
2answers
84 views

Categories without identities

What's the name of "categories without identities", i.e. of digraphs with just an associative binary operation on its "matching" arrows (disregarding identities)?
2
votes
1answer
183 views

Algebra terminology question

Suppose A is some algebraic structure, and x and y are two elements of the underlying set. Is there any more concise way of stating, "there exists an automorphism in A which maps x to y"?. It seems ...