3
votes
0answers
22 views

Reference for understanding coalgebra

I am trying to read this paper, but I have no knowledge of coalgebra and have just started to learn Category Theory so I am struggling to understand it. Are there any references that can explain ...
2
votes
1answer
39 views

Reference for $F$-algebras and induction?

I've been learning about $F$-coalgebras and coinduction from this fantastic paper, which has really helped me get a feel with its many examples. I'm starting to struggle with reconciling the ...
3
votes
1answer
51 views

Name for the embedding property

There is an exercise in Burris and Sankappanavar's "A Course in Universal Algebra": Problem: Find two algebras $\mathbf{A}_1$, $\mathbf{A}_2$ such that neither can be embedded in $\mathbf{A}_1 \times ...
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
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 ...
10
votes
2answers
156 views

Suggestions for a learning roadmap for universal algebra?

I think a useful combination of resources for universal algebra would ideally, when taken together: Provide ample motivation behind the various developments in the field. Either provide powerful ...
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 ...
3
votes
0answers
46 views

Seeking information about (category-theoretic) varieties, quasivarieties, and universal Horn classes.

I'm looking for a list of basic facts regarding (category-theoretic) varieties, quasivarieties, and universal Horn categories, as well as information about which forgetful functors preserve what. In ...
0
votes
1answer
54 views

Who first described commutative algebraic theories explicitly?

Lately, I've been thinking that the concept of a commutative algebraic theory is really, really important. So I'm curious; who had the honor of first discovering this concept? In particular, I'd like ...
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 ...
3
votes
3answers
319 views

New kind of identities?

I found a new kind of identities which are half logic and half algebraic while working on a proof of NP-completeness. They are like this: $$ \frac{a+mb}{n+m} < \frac{a}{n} \iff b < ...
8
votes
1answer
275 views

Combinatorics of term algebras

My question is about the number of terms of size $n$ in term algebras for an arbitrary (finite) signature. A signature is a map $\Sigma : S \rightarrow \mathbb{N}$ from a set $S$ of symbols. We ...