Georg Scheffers: Difference between revisions

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In [[mathematics]], more specifically in [[category theory]] - especially in [[internal category theory]] - an '''internal category'''<ref>Mac Lane, Moerdijk: Sheaves in Geometry and Logic, Springer</ref> in a category <math>C</math> with [[Pullback_(category_theory)|pullback]]s consists of the following data: two <math>C</math>-objects <math>C_0,C_1</math> named "object of objects" and "object of morphisms" respectively and four <math>C</math>-arrows <math>d_0,d_1:C_1\rightarrow C_0, e:C_0\rightarrow C_1,m:C_1\times_{C_0}C_1\rightarrow C_1</math> subject to coherence conditions expressing the axioms of category theory.
 
==See also==
* [[Enriched category]]
 
==References==
{{Reflist}}
*{{nlab|id=internal+category|title=Internal category}}
 
[[Category:Category theory]]

Revision as of 14:06, 18 October 2013

In mathematics, more specifically in category theory - especially in internal category theory - an internal category[1] in a category C with pullbacks consists of the following data: two C-objects C0,C1 named "object of objects" and "object of morphisms" respectively and four C-arrows d0,d1:C1C0,e:C0C1,m:C1×C0C1C1 subject to coherence conditions expressing the axioms of category theory.

See also

References

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  1. Mac Lane, Moerdijk: Sheaves in Geometry and Logic, Springer