# Tagged Questions

In a dagger category, what do we call an arrow $f$ satisfying $f \circ f^\dagger \circ f = f$? In $\mathrm{Rel}$ (and, more generally, an allegory) this is straightforwardly equivalent to $f \circ ... 1answer 62 views ### Completing a Partially Defined Associative Binary Operation This is more like a question about terminology. I would like to hear some recommendations of books that discuss algebraic structures with one partially defined associative binary operation, and the ... 1answer 37 views ### Terminology for a weaked vector space Let$S$be a semigroup on which acts$\mathbb{R}_{\geq0}$. Does this structure has a name? For example$S$can be the set of convex bodies in$\mathbb{R}^n$with the Minkowsky sum. 1answer 58 views ### Is there a standard name for this semigroup? Given a semigroup$X,$we can form a new semigroup$Y$by asserting that: the carrier of$Y$is the set$X^2$, and the law of composition in$Y$is given by$(a,b)(a',b')=(aa',b'b).$Finally, ... 1answer 53 views ### Definition of tautological action What is the precise meaning of the term 'tautological action' as used for example in this Wikipedia page in the context of semigroup actions? For reference the particular sentence is: "A ... 2answers 116 views ### What should I call this commutative monoid of order three? I'm looking for a name for the monoid given by the following table: $$\begin{array}{c|ccc}&1&a&b\\ \hline 1&1&a&b\\ a&a&1&b\\ b&b&b&b \end{array}$$ ... 2answers 123 views ### Is there a name for a semigroup whose idempotents form a subsemigroup? For a semigroup$S,$I will denote by$E(S)$the set of all idempotents of$S$. For$X\subseteq S,$let$X^2$mean$\{xy\,|\,x,y\in X\}.$Is there a name for the class of semigroups$S$such that ... 0answers 74 views ### Is there a name for a subset$S$of a group or a semigroup such that every two elements of$S$commute? Let$G$be a group and$S$its subset. I would like to consider the following condition on$S$. For every$x,y\in S,$we have$xy=yx.$This is trivially equivalent to$S\subseteq C(S).$The ... 1answer 151 views ### Semigroups of matrices with zeroes and a single 1 I stumbled upon this while reviewing a Harvard lecture on abstract algebra. What I want to know is if these semigroups are known and, if so, what they are called. I've checked the assertions below for ... 1answer 73 views ### Nomenclature for distributive action between semigroups Let$(G,*)$and$(H,+)$be semigroups. Let$\cdot$be an action of$G$on$H$, such that$\cdot$distributes over$*$. [I.e.,$(g_1 * g_2) \cdot h = g_1*(g_2\cdot h)$, and$g\cdot(h_1+h_2) = (g\cdot ...
Let $S$ be a (commutative) semigroup with distinguished element 0 such that $ab=0$ for $a,b\in S.$ Of course this is a very simple family of semigroups, defined only by their cardinality. Does it ...