What are the morphisms in the category of group presentations?
2026-03-27 02:02:58.1774576978
Morphisms in the category of group presentations
167 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in GROUP-THEORY
- What is the intersection of the vertices of a face of a simplicial complex?
- Group with order $pq$ has subgroups of order $p$ and $q$
- How to construct a group whose "size" grows between polynomially and exponentially.
- Conjugacy class formula
- $G$ abelian when $Z(G)$ is a proper subset of $G$?
- A group of order 189 is not simple
- Minimal dimension needed for linearization of group action
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
- subgroups that contain a normal subgroup is also normal
- Could anyone give an **example** that a problem that can be solved by creating a new group?
Related Questions in CATEGORY-THEORY
- (From Awodey)$\sf C \cong D$ be equivalent categories then $\sf C$ has binary products if and only if $\sf D$ does.
- Continuous functor for a Grothendieck topology
- Showing that initial object is also terminal in preadditive category
- Is $ X \to \mathrm{CH}^i (X) $ covariant or contravariant?
- What concept does a natural transformation between two functors between two monoids viewed as categories correspond to?
- Please explain Mac Lane notation on page 48
- How do you prove that category of representations of $G_m$ is equivalent to the category of finite dimensional graded vector spaces?
- Terminal object for Prin(X,G) (principal $G$-bundles)
- Show that a functor which preserves colimits has a right adjoint
- Show that a certain functor preserves colimits and finite limits by verifying it on the stalks of sheaves
Related Questions in GROUP-PRESENTATION
- What is the intersection of the vertices of a face of a simplicial complex?
- Automata defined by group presentations.
- Terminology: reversing the order of the generators.
- Is there a general way to simplify such group presentations (Free Abelian Group with Relations)?
- Proof of a relation of Braid groups
- Prove G is a nonabelian group of order 20
- Is this specific group finite?
- Isomorphy of simple groups of order 360 : a proof with a presentation
- Centralizers of non-central elements of a special group
- Find the group given the presentation
Related Questions in COMBINATORIAL-GROUP-THEORY
- Putnam 2016 Question A5 Finite Group Theory
- Is there a general way to simplify such group presentations (Free Abelian Group with Relations)?
- The context & motivation for the Tits alternative in combinatorial group theory
- Prove G is a nonabelian group of order 20
- Making linear groups trivial by adding an equal number of generators and relations
- An algorithm determining whether two subgroups of a free group are automorphic
- If the deficiency of a presentation $P$ is $0$ and $P$ is aspherical, then the deficiency of the group $P$ defines is $0$.
- Solution book for "Presentations of Groups" by D. L. Johnson
- Notational confusion about HNN-extensions: $G=K \ast_{H,t}$.
- What is this group $G=\langle a,b,c\mid a^2=1, b^2=1, c^2=ab\rangle$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
I've never heard of the "category of group presentations". If I had to guess what was intended by such a name, it would be a category whose objects are diagrams
$$ F \to G $$
where $F$ and $G$ are free groups. Correspondingly, the morphisms ought to be morphisms of diagrams: that is, commutative squares
$$ \begin{matrix} F &\to& G \\ \downarrow & & \downarrow \\ F' &\to& G' \end{matrix} $$