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Presheaf topos
Codex
(
@codex,
0
)
...
Foundations of mathematics
Category theory
Category
Functor
Functor category
Presheaf category
2026-10-03
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Every
presheaf category
is
a
topos
.
Finite limits
are
pointwise
; the exponential is
(
G
F
)
(
C
)
=
Nat
(
y
C
×
F
,
G
)
,
(1)
and the
subobject classifier
assigns to
C
the
set
of sieves on
C
.
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(9)
Presheaf category
Functor category
Functor
Category
Category theory
Foundations of mathematics
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2019
/
iii
/
Paper 119
/
6
/
a
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2019
/
iii
/
Paper 119
/
6
/
b
/
Solution
Representable presheaves are the tiny objects of an idempotent-complete finite-product category
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