# Tagged Questions

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### Does the category PCM (partial commutative monoids) have a closed symmetric monoidal product?

A partial commutative monoid (PCM) is, roughly speaking, a set with a partially defined binary operation that is as associative as it can be (given that not all products are defined) and commutative. ...
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### First-countable topological monoids without local absorbing elements whose topology is induced by a semimetric

This is a follow up of Question 163246. For the reader's convenience, let me first copy&paste some basic definitions. We let a semimetric on a set $X$ be a function $d: X \times X \to [0,\infty]$ ...
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### If $(\mathbb M, \tau)$ is a topological monoid, is $\tau$ always induced by a [left] subinvariant semimetric?

Let me start by recalling some basic definitions (just for the sake of avoiding misunderstandings due to the vocabulary of the post). Basically following some ideas of W. Lawvere (but not his ...
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A linearly ordered (shortly, l.o.) monoid is a triple $\mathbb M = (M, \cdot, \le)$ for which $(M, \cdot)$ is a (multiplicatively written) monoid and $\le$ is a total order on $M$ such that $xy < ... 1answer 352 views ### Study of convex polytopes via commutative algebra Let$P \subset \mathbb{R}^d$be any convex polytope with integral vertices, and let$M$be the additive submonoid of$\mathbb{R}^{d+1}$which is generated by$\{ (v,1) : v \in P \cap \mathbb{Z}^d \}$. ... 1answer 168 views ### What is the formula for the commutative multiplication on CP(infinity)? There is a classic formula for maps$\mathrm{CP}(r) \times \mathrm{CP}(s) \to \mathrm{CP}(r+s)$or maybe$r+s+1$using Plücker coordinates - IF memory serves. In the limit we get the abelian ... 2answers 146 views ### Equivalence relations in suplattices I am wondering about generalisations of the concept of equivalence relations to suplattices. Here is my motivation: Given a set$X$. The powerset$\mathcal{P}(X)$is a suplattice. For suplattices ... 0answers 87 views ### Reasoning about “approximately” associative structures and “almost monoids”. If$(M,+)$is a monoid then it obeys the laws: $$m_1 + 0 = 0 + m_1 = m_1$$ $$m_1+(m_2+m_3)=(m_1+m_2)+m_3$$ But what if I have a structure$(A,+)$that is almost a monoid, but not quite. For ... 2answers 216 views ### An operation on binary strings Consider the “product”$\gamma = \alpha \times \beta$of two binary strings$\alpha$,$\beta\in \lbrace 0,1\rbrace^+$which one gets by replacing every 1 in$\beta$by$\alpha$and each ... 1answer 347 views ### Question about topological monoid maps Let Mon be the category of topological monoids. I am happy to work with the model structure mentioned here: Model Structure/Homotopy Pushouts in topological monoids?. I'm looking for a reference ... 1answer 159 views ### Kernel elements for the Grothendieck group map of a commutative monoid This is just a nomenclature question. Let$T$be a commutative monoid, and let$T^*$be its Grothendieck group. That is,$T^* \cong T \times T \ / \sim$, where$(s,s') \sim (t, t')$if$s+t'+e = ...
It is well-known that the (augmented) simplex category is the universal monoidal category with a monoid object. What about a commutative analogue? Consider the category $\mathsf{FinSet}$ of finite ...