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New posts in homological-algebra
Getting the most general form of Mayer-Vietoris from the axioms of homology
reference-request
algebraic-topology
homological-algebra
homology-cohomology
Isomorphic cokernels giving isomorphic kernels
commutative-algebra
homological-algebra
exact-sequence
Ext and Tor duality
reference-request
algebraic-topology
commutative-algebra
homological-algebra
Being direct summand of free module implies having dual basis.
abstract-algebra
modules
homological-algebra
projective-module
free-modules
An example of computing Ext
homological-algebra
Hochschild homology - motivation and examples
abstract-algebra
homological-algebra
On equivalent definitions of Ext
category-theory
homological-algebra
abelian-categories
Signs in the tensor product and internal hom of chain complexes
intuition
homological-algebra
tensor-products
Why is the definition of $\lim^1$ via a cokernel the first derived functor of $\lim$?
homological-algebra
derived-functors
Motivation for the mapping cone complexes
algebraic-topology
intuition
homological-algebra
A direct product of projective modules which is not projective
ring-theory
modules
homological-algebra
projective-module
$B$ a chain complex of free abelian groups and $C$ a chain complex such that $H_n(C)=0$. Then any chain map from $B$ to $C$ homotopic to the zero map
algebraic-topology
homological-algebra
Is homology an adjoint functor?
category-theory
homology-cohomology
homological-algebra
Additive functors preserve split exact sequences
homological-algebra
Alternative construction of Direct Limit
commutative-algebra
category-theory
homological-algebra
Why are we interested in cohomology?
general-topology
algebraic-topology
soft-question
homological-algebra
homology-cohomology
showing exact functors preserve exact sequences (abelian categories, additive functors, and kernels)
category-theory
homological-algebra
abelian-categories
Motivation for Koszul complex
commutative-algebra
homological-algebra
History behind Exact Sequences.
math-history
homological-algebra
motivation
abstract-algebra
Ext between two coherent sheaves
algebraic-geometry
homological-algebra
derived-functors
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