# Questions tagged [universal-algebra]

The study of algebraic structures and properties applying to large classes of such structures. For example, ideas from group theory and ring theory are extended and considered for structures with other signatures (systems of basic or fundamental operations).

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### Given a lattice L with n elements, are there finite groups H < G such that L $\cong$ the lattice of subgroups between H and G?

**17**

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### Why did Bourbaki not use universal algebra?

**13**

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### The free complete lattice on three generators, beyond ZF

**13**

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### Is there a finite equational basis for the join of the commutative and associative equations?

**12**

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### Birkhoff's HSP theorem in categories other than $\mathbf{Set}$

**11**

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### When can we tell if PROPs, Algebraic Theories, etc. are faithfully detected in a given category?

**9**

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### Equational theory in the signature (+,*,0,1) of sedenions and beyond

**9**

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### "Generalized theory of polynomials" for a given commutative Lawvere Theory

**8**

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### What is going on in the field of algebraic logic these days?

**8**

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### Is there any theorem achieving Conway's "Mathematician's Liberation Movement"

**8**

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### Which semirings have enough injectives in their category of modules?

**8**

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### Varieties of groups with certain properties

**8**

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### To what kind of generalized Lawvere theory does the "free cartesian closed category" 2-monad on $\mbox{Cat}_g$ correspond?

**8**

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### General approaches to extension theorems as Caratheodory

**8**

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### When can I assure that the representation theory of a PROP is faithful?

**8**

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### The name for a partial order

**8**

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### Counting and understanging commuting functions.

**7**

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### Were algebraic theories and abstract clones defined independently?

**7**

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### Invariant theory in universal algebra

**7**

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### Is there a theory of algebraic universal algebra?

**7**

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### What Spec-like functors are there?

**7**

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### Hemi-semi direct product of racks or quandles

**7**

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### Finitely presented algebras with isomorphic semilattices of congruences

**7**

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### When are the categories of algebras over props (co)complete?

**7**

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### Universal anti-Horn classes?

**7**

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### Adjunction algebra - is there anything similar to this in algebra?

**7**

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### Binary Operation on a Cubic Surface

**7**

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### Invertible elements in generalized fields

**7**

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### Undecidability degree of some elementary theories (two equivalence relations, ...)

**6**

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### Birkhoff's theorem with language expansion?

**6**

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### An adjunction between monads on $\mathcal{C}$ and presentable categories under $\mathcal{C}$

**6**

**1**answer

### Does the likelihood of these tables exist?

**6**

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### Can finite binary self-distributive algebras fit into small $n$-ary self-distributive algebras?

**6**

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### Universal identities on cubic surfaces or hypersurfaces

**6**

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### Why are there so few elements in the classical Laver tables with period 32?

**6**

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### What is the probability that a thread in the inverse limit of classical Laver tables is induced by a rank-into-rank embedding?

**5**

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### Axiomatizability of image of functor

**5**

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### Cohomology without comonad?

**5**

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### Algebraic/relational structures produced using evolutionary/machine learning algorithms?

**5**

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### Permutative Yang-Baxter monoids

**5**

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### What are some examples of inner endomorphisms?

**5**

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### How to count Isomorphism Types of arbitrary structures?

**5**

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### Pseudovarieties of monoids

**5**

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### Embedding of relatively free groups of bigger rank into ones of smaller rank

**5**

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### The graph of algebraic theories

**4**

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### Minimization of second-order unifiers

**4**

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### Polynomial objects in any concrete category

**4**

**1**answer

### Reversible varieties

**4**

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### Closing Subsets Under Operations

**4**

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