nLab
simplicial abelian group

Contents

Context

Homotopy theory

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

Group Theory

Contents

Definition

A simplicial abelian group is

Properties

Basic properties

Proposition

(free simplicial abelian group-adjunction)
There is a pair of adjoint functors (a free\dashvforgetful-adjunction)

sAbfrgt()sSet sAb \underoverset {\underset{ frgt }{\longrightarrow}} {\overset{\mathbb{Z}(-)}{\longleftarrow}} {\;\;\;\;\;\bot\;\;\;\;\;} sSet

between SimplicialAbelianGroups and SimplicialSets, where

This is a Quillen adjunction with respect to the classical model structure on simplicial sets and the projective model structure on simplicial abelian groups.

More properties

Last revised on July 14, 2021 at 06:57:10. See the history of this page for a list of all contributions to it.