Difference between revisions of "Category (category theory)"
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** (identity) For and object <math>X</math>, there is an identity morphism <math>1_X:X\to X</math> such that for any <math>f:A\to B</math>: <cmath>1_B\circ f = f = f\circ 1_A.</cmath> | ** (identity) For and object <math>X</math>, there is an identity morphism <math>1_X:X\to X</math> such that for any <math>f:A\to B</math>: <cmath>1_B\circ f = f = f\circ 1_A.</cmath> | ||
+ | The class of all morphisms of <math>\mathcal{C}</math> is denoted <math>\text{Hom}(\mathcal{C})</math> | ||
{{stub}} | {{stub}} | ||
[[Category:Category theory]] | [[Category:Category theory]] |
Revision as of 00:12, 2 September 2008
A category, , is a mathematical object consisting of:
- A class, of objects.
- For every pair of objects , a class of morphisms from to . (We sometimes write to mean .)
- For every three objects, , a binary operation called composition, which satisfies:
- (associativity) Given , and we have
- (identity) For and object , there is an identity morphism such that for any :
The class of all morphisms of is denoted This article is a stub. Help us out by expanding it.