Last Updated：2022/12/24
Category theory also contributes new proof techniques, such as diagram chasing or arguments by duality; Steenrod called these methods “abstract nonsense.”³ The aim of this text is to introduce the language, philosophy, and basic theorems of category theory. A complementary objective is to put this theory into practice: studying functoriality in algebraic topology, naturality in group theory, and universal properties in algebra.
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Category
theory
also
contributes
new
proof
techniques,
such
as
diagram
chasing
or
arguments
by
duality;
Steenrod
called
these
methods
“abstract
nonsense.”³
The
aim
of
this
text
is
to
introduce
the
language,
philosophy,
and
basic
theorems
of
category
theory.
A
complementary
objective
is
to
put
this
theory
into
practice:
studying
functoriality
in
algebraic
topology,
naturality
in
group
theory,
and
universal
properties
in
algebra.
