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Monomorphisms, Epimorphisms, and Pull-Backs

# Monomorphisms, Epimorphisms, and Pull-Backs,10.1017/S1446788700005693,Journal of The Australian Mathematical Society,G. M. Kelly

Monomorphisms, Epimorphisms, and Pull-Backs
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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 Lattice-Finite 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...

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