All Questions
Tagged with magma category-theory
8
questions
4
votes
1
answer
204
views
Surjective homomorphism into a magma confers all the algebraic properties of the domain
Let $A$ be your favorite algebraic object (group, abelian group, rng, ring, commutative ring, field, module, vector space). Let $M$ be a magma. The image of a "homomorphism" $\phi : A \to M$ ...
- 1,751
3
votes
1
answer
224
views
Is there a category of partially defined binary operations?
A magma is a set $Y$ with a binary operation $m:Y \times Y \rightarrow Y.$ A partial magma is the same idea, but where the binary operation $m$ may not be defined on some pairs of elements of $Y.$ My ...
- 1,659
5
votes
3
answers
753
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What is difference between idempotent magma and unital magma?
I don't understand well in what way idempotent element is wired to identity element in a magma context.
idempotent: $x \cdot x = x$
identity element: $1 \cdot x = x = x \cdot 1$
For example ...
- 65
4
votes
1
answer
387
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Elegant approach to coproducts of monoids and magmas - does everything work without units?
From this answer by Martin Brandenburg I learned an elegant way of constructing and describing elements of coproducts of monoids. There he writes this construction shows the existence of colimits in ...
- 14k
2
votes
1
answer
127
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Concretely describing the arrow $A\amalg B\to A\times B$ for nonlinear algebraic theories
I'm reading about unital categories to get a better understanding of nonlinear algebraic categories like groups, monoids, semigroups, magmas etc.
A unital category is a pointed finitely complete ...
- 14k
2
votes
1
answer
1k
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Associativity in category theory [closed]
In Category Theory, the composition of morphisms must be associative. What would happen if we give up this associative law? For example Lie algebras are vector spaces with non-associative binary ...
- 69
4
votes
2
answers
165
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Are epimorphisms in the category of magmas surjective?
The question says it all, but let me recall the definitions.
A magma $(X, \cdot)$ is a set $X$ with a binary operation $\cdot \colon X \times X \to X$ (without any further assumptions like ...
- 12.3k
4
votes
1
answer
207
views
How to describe free magmas in more structuralist terms?
Given a generating set $G$ (assume for simplicitly it consists entirely of urelements), the free magma on $G$ can be described concretely as follows.
Its underlying set is the least $U \supseteq G$ ...
- 68.1k