# Abstract initiality

Commentationes Mathematicae Universitatis Carolinae (2000)

- Volume: 41, Issue: 3, page 575-583
- ISSN: 0010-2628

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topSchröder, Lutz, and Herrlich, Horst. "Abstract initiality." Commentationes Mathematicae Universitatis Carolinae 41.3 (2000): 575-583. <http://eudml.org/doc/248620>.

@article{Schröder2000,

abstract = {We study morphisms that are initial w.r.t. all functors in a given conglomerate. Several results and counterexamples are obtained concerning the relation of such properties to different notions of subobject. E.g., strong monomorphisms are initial w.r.t. all faithful adjoint functors, but not necessarily w.r.t. all faithful monomorphism-preserving functors; morphisms that are initial w.r.t. all faithful monomorphism-preserving functors are monomorphisms, but need not be extremal; and (under weak additional conditions) a morphism is initial w.r.t. all faithful functors that map extremal monomorphisms to monomorphisms iff it is an extremal monomorphism.},

author = {Schröder, Lutz, Herrlich, Horst},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {initial morphism; (extremal) monomorphism; faithful functor; semicategory; initial morphism; monomorphism; faithful functor; semicategory},

language = {eng},

number = {3},

pages = {575-583},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Abstract initiality},

url = {http://eudml.org/doc/248620},

volume = {41},

year = {2000},

}

TY - JOUR

AU - Schröder, Lutz

AU - Herrlich, Horst

TI - Abstract initiality

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2000

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 41

IS - 3

SP - 575

EP - 583

AB - We study morphisms that are initial w.r.t. all functors in a given conglomerate. Several results and counterexamples are obtained concerning the relation of such properties to different notions of subobject. E.g., strong monomorphisms are initial w.r.t. all faithful adjoint functors, but not necessarily w.r.t. all faithful monomorphism-preserving functors; morphisms that are initial w.r.t. all faithful monomorphism-preserving functors are monomorphisms, but need not be extremal; and (under weak additional conditions) a morphism is initial w.r.t. all faithful functors that map extremal monomorphisms to monomorphisms iff it is an extremal monomorphism.

LA - eng

KW - initial morphism; (extremal) monomorphism; faithful functor; semicategory; initial morphism; monomorphism; faithful functor; semicategory

UR - http://eudml.org/doc/248620

ER -

## References

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