Foundations of the Theory of Categories

Kurosh, A.G.; Livshits, A Kh; Shul'geifer, E. G.

doi:10.1070/rm1960v015n06abeh001116

Cited by 35 publications

(10 citation statements)

References 17 publications

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“…Applying v 0 , we can define the notion of internal direct decomposition and internal direct factor of A similarly to the case of groups (cf., e.g., Kurosh [21], p. 106).…”

Section: L-varieties and L * -Varietiesmentioning

confidence: 99%

On a theorem of Cantor-Bernstein type for algebras

Jakubík¹

2008

Czech Math J

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“…Applying v 0 , we can define the notion of internal direct decomposition and internal direct factor of A similarly to the case of groups (cf., e.g., Kurosh [21], p. 106).…”

Section: L-varieties and L * -Varietiesmentioning

confidence: 99%

On a theorem of Cantor-Bernstein type for algebras

Jakubík¹

2008

Czech Math J

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“…~') In view of terminological differences appearing in the literature we wish to emphasize that the terms "monomorphism" and "epimerphism" are used in agreement with [9], see also [1]: A map ~: X-~ Y in the category ~ is a monomorphism if, for all ZE~ and maps g, h : Z --> X in ~, ]g ~/h implies g ~ h; and dually for epimorphisms.…”

Section: Prol~osition 13 Left Equalizers Are Monomorphisms Right Ementioning

confidence: 99%

Group-like structures in general categories II equalizers, limits, lengths

Eckmann¹,

Hilton²

1963

Math. Ann.

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“…As mentioned in the introduction, we can now provide a new proof of the following result of La Martin [6]; our proof is a topologized version of the original proof ( [5]; see also [9]) that epimorphisms of groups are surjective.…”

Section: Corollary With the Quotient Topology Determined By P G Is mentioning

confidence: 99%