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Monomorphisms, Epimorphisms, and PullBacks
Monomorphisms, Epimorphisms, and PullBacks,10.1017/S1446788700005693,Journal of The Australian Mathematical Society,G. M. Kelly
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Monomorphisms, Epimorphisms, and PullBacks
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Citations: 32
)
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G. M. Kelly
Journal:
Journal of The Australian Mathematical Society  J AUST MATH SOC
, vol. 9, no. 12, 1969
DOI:
10.1017/S1446788700005693
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www.journals.cambridge.org
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Citation Context
(7)
...Recall from [
K1
] that, in any category, a morphism a : A ! B is called orthogonal to a morphism b : C ! D, if for every commutative square...
...Recall from [
K1
] that strong epimorphisms are defined as those morphisms that are orthogonal to every monomorphism...
...Therefore regular epimorphisms in Mndfin(Set) are closed under composition and thus strong epimorphisms coincide with regular epimorphisms in Mndfin(Set) by Proposition 3.8 of [
K1
]...
PANAGIS KARAZERIS
,
et al.
DENSE MORPHISMS OF MONADS
...The following results 2.6 and 2.7, which will be needed in Section 6 are taken from [14]. Parts of them can also be found in [
12
]...
Viviana A. Zelizer
,
et al.
Relations and Categories
...with h :¼ ker p. Then g is a kernel by [
6
], Proposition 5.2...
Wolfgang Rump
.
Global Theory of LatticeFinite Noetherian Rings
...(ii)⇒(i) is proved in [
K
], [Ri], [T], while the equivalence (i)⇔(iii) is proved in [Ri]...
...α β
K
with monomorphisms i1 ,i 2 ,i 3 such that the bottom part is an equalizer diagram and, moreover, there exist d, d� ∈ D\B with b−1α(d )= b−1 1 β(d )a ndα(d � )b� = β(d� )b� 1 .I t is easy to see that for the element x = d� td of D � B E we have (α � B 1E)(x )=( β � B 1E)(x)...
DALI ZANGURASHVILI
.
THE STRONG AMALGAMATION PROPERTY AND (EFFECTIVE) CODESCENT MORPHISMS
...We shall call a map p: A ~ K in ¢4 a surjection (the more usual name see [
20
]  is strong epimorphism) if it factorizes through no proper subobject of K. Every surjection is an epimorphism, and every regular epimorphism (that is, every coequalizer), and in particular every retraction, is a surjection; the converses are false in general...
A. Carboni
,
et al.
Some remarks on Maltsev and Goursat categories
References
(1)
Structure of categories
(
Citations: 22
)
John R. Isbell
Journal:
Bulletin of The American Mathematical Society  BULL AMER MATH SOC
, vol. 72, no. 1966, pp. 619655, 1966
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Citations
(32)
Elementary varieties and existence of flat covers
(
Citations: 1
)
Wolfgang Rump
Journal:
Journal of Algebra  J ALGEBRA
, vol. 322, no. 6, pp. 21312149, 2009
Abelian categories in dimension 2
(
Citations: 7
)
Mathieu Dupont
Published in 2008.
DENSE MORPHISMS OF MONADS
PANAGIS KARAZERIS
,
RI VELEBIL
Published in 2007.
Effective codescent morphisms, amalgamations and factorization systems
Dali Zangurashvili
Journal:
Journal of Pure and Applied Algebra  J PURE APPL ALG
, vol. 209, no. 1, pp. 255267, 2007
Relations and Categories
(
Citations: 2
)
Viviana A. Zelizer
,
Charles Tilly
Journal:
Psychology of Learning and Motivation  PSYCH LEARN MOTIVADV RES TH
, vol. 47, pp. 131, 2006