**1**

vote

**4**answers

840 views

### Is monomorphism going in both directions sufficient for isomorphism?

In category theory, it seems that a monomorphism from $A$ to $B$ and one from $B$ to $A$ should be enough to guarantee isomorphy, but it doesn't seem to be so. (If I'm right then there's something ...

**9**

votes

**2**answers

643 views

### Right actions of operads and monads

Given an operad $A$, there is an associated monad $M_A$ given by $M_A(X) = \coprod_n A(n) \otimes X^{\otimes n}$ such that being an $A$-algebra and being an algebra over the monad $M_A$ is the same ...

**2**

votes

**1**answer

478 views

### Higher-order, multi-sorted, non purely equational version of universal algebra ?

I have been looking around, unsuccessfully, for generalizations of universal algebra based on higher-order logic (rather than first order) and where the relations are not purely equational. ...

**3**

votes

**2**answers

270 views

### Terminology: Name for a homomorphism from the free object?

Is there a standard name for taking a homomorphism from the free object over an algebraic structure? Roughly speaking, this should amount to evaluation of any element of the free object under the ...

**1**

vote

**1**answer

518 views

### Coequalizer in the category of primitive recursive functions

What does a coequalizer in the category of primitive recursive functions look like? I know that in Set, a coequalizer is a minimum congruence but...what is it in particular in the category of ...

**4**

votes

**2**answers

453 views

### Is every lattice the fixed-point set of an order endomorphism of ⋄^n?

(Asked by Nathaniel Hellerstein on the Q&A board at JMM)
Let ⋄ be the 4 element lattice
τ
/ \
i j
\ /
f
Is every lattice isomorphic to the fixed point lattice of some ...