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 with pullbacks consists of the following data: two -objects named "object of objects" and "object of morphisms" respectively and four -arrows subject to coherence conditions expressing the axioms of category theory.
See also
References
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- ↑ Mac Lane, Moerdijk: Sheaves in Geometry and Logic, Springer