Does the tensor product of dg algebras have a universal property? I have not seen anything about this in the literature.
2026-03-25 16:03:39.1774454619
Universal property of tensor product of dg algebras
164 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
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 HOMOLOGICAL-ALGEBRA
- How does $\operatorname{Ind}^G_H$ behave with respect to $\bigoplus$?
- Describe explicitly a minimal free resolution
- $A$ - dga over field, then $H^i(A) = 0, i > 1$ implies $HH_i(A) = 0, i < -1$
- Tensor product $M\otimes_B Hom_B(M,B)$ equals $End_B(M)$, $M$ finitely generated over $B$ and projective
- Group cohomology of $\mathrm{GL}(V)$
- two maps are not homotopic equivalent
- Existence of adjugant with making given natural transformation be the counit
- Noetherian property is redundant?
- What is the monomorphism that forms the homology group?
- Rational points on conics over fields of dimension 1
Related Questions in UNIVERSAL-PROPERTY
- Where there exists a unique arrow from $n: L \to K$ as a UMP can we reverse $n$?
- Exponentiation property of the modulo operator
- Cartesian product uniqueness (up to bijection). Need to clarify two questions.
- Theorem about Universal Property for Vector Spaces
- What are the obtained consequences in mathematics if the antiderivative of $e^{-x²}$ and $e^{x²}$ expressed as elementary functions?
- Closed form of $I(a)=\int_{0}^a {(e^{-x²})}^{\operatorname{erf}(x)}dx $ and is it behave similar with error function?
- What is the asymptotic series of :$I(a)=\int_{0}^a {(e^{-x²})}^{\operatorname{erf}(x)}dx $ and does it have a complementary function?
- Why Owen's selected this function $f(h,x)=\frac{e^{-\frac 12 h^2(1+x²)}}{1+x²}$ for integration?
- Constructing a solenoid to satisfy its universal property as a projective limit over circles
- The Universal Property of a Universal C$^{*}$-algebra
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?
If $C$ is any symmetric monoidal category, then the tensor product of commutative algebras in $C$ is their coproduct. The tensor product of algebras in $C$, not necessarily commutative, is the "commutative coproduct": We have to add to the universal property that the test morphisms commute with each other. Now apply this to $C=$ chain complexes.