Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Koszul duality in algebraic topology - an historical perspective   We survey the topology which led to the original bar and cobar constructions,
for both associative algebras and coalgebras and for Lie algebras and
commutative coalgebras. These constructions are often viewed as part of the
larger theory of Koszul duality of operads, so this survey is meant to offer an
historical perspective on the most prominent cases of that theory. We also
explain recent work which shows that Hopf/linking invariants for homotopy are
at the heart of the duality between commutative algebras and Lie coalgebras.

16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con