# 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).

**2**

**2**answers

### Finitary endofunctors: “Support” of elements of $TM$ where $T:\mathrm{Set}\to\mathrm{Set}$ is finitary

**9**

**0**answers

### Finitely presentable grids and co-presentable topological spaces

**0**

**3**answers

### value (element of an algebra), constant, variable, ground and non-ground terms, free algebras : there is a need for clarification

**0**

**1**answer

### Finitely presented algebra [closed]

**10**

**3**answers

### Comparing the existing formulations of universal algebra and their levels of generality

**10**

**0**answers

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

**2**

**0**answers

### Minimizing all aspects of the definition of Boolean algebra

**19**

**2**answers

### Why does abelianization preserve finite products, really?

**3**

**0**answers

### Proving interpolation results through amalgamation

**9**

**2**answers

### Varieties where every algebra is projective?

**3**

**1**answer

### On the tree-ishness of magmas and the stringiness of groups

**2**

**0**answers

### Union star symbol in set theory

**10**

**1**answer

### Generalized cancelation properties ensuring a monoid embeds into a group

**0**

**1**answer

### Ordering preserved by an inverse frame homomorphism

**1**

**0**answers

### Equational identities of sedenions and beyond in the signature of multiplication

**3**

**2**answers

### Are gyrogroups useful for anything else other than the Einstein velocity addition rule?

**5**

**0**answers

### Cohomology without comonad?

**1**

**2**answers

### Example of idempotent left quasigroups which are right-distributive but not left-distributive

**0**

**0**answers

### Closedness of certain functional form; solvability of linear system; equationally compactness

**3**

**1**answer

### What is the name for Boolean algebra's version of $\models$ between sets of identities and identities?

**-2**

**1**answer

### Is equational logic in universal algebra a proof system not a logic system?

**2**

**0**answers

### Varieties where any subalgebra is a regular sub-object

**23**

**1**answer

### Are there axioms satisfied in commutative rings and distributive lattices but not satisfied in commutative semirings?

**3**

**1**answer

### Characterisation of presentations for varietal large equational theories

**5**

**1**answer

### “Tietze-like transformations” for defining interesting bijections between algebraic structures

**4**

**0**answers

### Polynomial objects in any concrete category

**13**

**0**answers

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

**7**

**0**answers

### Invariant theory in universal algebra

**7**

**1**answer

### Jordan algebra identities

**5**

**3**answers

### Is the class of power-associative binars finitely axiomatizable?

**1**

**0**answers

### Morphism of sketches inducing a (co)reflective subcategory

**3**

**2**answers

### Polynomial identities of supercommutative-gradable algebras

**1**

**1**answer

### Indecomposable weirdos (cnt.)

**-1**

**1**answer

### Topological connected eccentrics, not homeomorphic to commutative Lie groups

**-1**

**2**answers

### Weirdos but algebraic

**15**

**1**answer

### What is a module over a Boolean ring?

**9**

**2**answers

### Comparing “axiomatized function spaces”

**3**

**2**answers

### Explicit lifting characterization of complete lattices among posets?

**9**

**1**answer

### Why is the theory of small categories not algebraic?

**3**

**0**answers

### When will a monad satisfy Moggi’s “equalizer” property?

**8**

**1**answer

### Birkhoff's completeness theorem put into practice

**7**

**1**answer

### Does Higman's embedding theorem hold inside group varieties?

**6**

**0**answers

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

**3**

**1**answer

### Is finite verbal subgroup equivalent to finite index of marginal subgroup?

**5**

**2**answers

### Universal property of the cocomplete category of models of a limit sketch

**2**

**1**answer

### Non-abelian variety of groups in which finite groups are abelian

**9**

**0**answers

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

**6**

**1**answer

### Can a compact object be a nontrivial self-retract?

**1**

**1**answer

### Bounds for Khukhro-Makarenko theorems

**2**

**0**answers