New posts in homological-algebra

Singular $\simeq$ Cellular homology?

algebraic-topology homological-algebra

When does tensor product have a (exact) left adjoint?

commutative-algebra category-theory modules homological-algebra tensor-products

Can we see directly from the cocycle condition that 2-cocycles are symmetric?

group-theory finite-groups homological-algebra homology-cohomology group-cohomology

Simple, Cyclic and Projective Modules

abstract-algebra modules homological-algebra projective-module

Question about mapping cones in homology theory

algebraic-topology homology-cohomology homological-algebra

Computing the homology of genus $g$ surface, using Mayer-Vietoris

algebraic-topology homology-cohomology homological-algebra

Isomorphism in cohomology is an isomorphism in homology

algebraic-topology homological-algebra homology-cohomology

Wedge sum of spheres is the quotient $X^n/X^{n-1}$

category-theory homology-cohomology homological-algebra cw-complexes

Long exact sequence in homology: naturality=functoriality?

homological-algebra exact-sequence

Correspondence between Ext group and extensions (from Weibel's book)

abstract-algebra notation homological-algebra

Exercise 1.1.3 in Charles Weibel’s book “An Introduction to Homological Algebra”

vector-spaces homological-algebra homology-cohomology

Weibel 1.4.1: Show that acyclic bounded below chain complexes of free R-modules are always split exact.

homological-algebra

Question 43 in section 2.2 of Hatcher's Algebraic Topology

algebraic-topology homological-algebra exact-sequence

Exercise in Spanier to get universal coefficient theorem for cohomology with local coefficients

algebraic-topology homology-cohomology homological-algebra

Does the splitting lemma hold without the axiom of choice?

homological-algebra homological-algebra abelian-groups abelian-groups axiom-of-choice axiom-of-choice

$f_*$ induces an isomorphism in homology iff the mapping cone of $f_*$ is contractible.

homological-algebra homology-cohomology

$\text{Ext}(H, \mathbb{Z})$ is isomorphic to the torsion subgroup of $H$ if $H$ is finitely generated

algebraic-topology homological-algebra

Universal coefficient theorem with ring coefficients

algebraic-topology homological-algebra homology-cohomology

Computing $\operatorname{Ext}^{1}_{\mathbb{Z}}(\mathbb{Q},\mathbb{Z})$

homological-algebra