scratch
§
Orthogonal Factorization Systems
created 2022-04-03
For a category
C
C
C
, a factorization system consists of sets of morphisms
(
E
,
M
)
(E, M)
(
E
,
M
)
such that:
E
,
M
E, M
E
,
M
contain all isos.
E
,
M
E, M
E
,
M
are closed under composition.
every morphism in
C
C
C
can be factored as
M
∘
E
M \circ E
M
∘
E
The factorization is
functorial
:
Reference: Riehl on factorization systems
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