Difference between revisions of "Math equation demo"
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In more explicit terms, the equaliser consists of an object ''E'' and a morphism ''eq'' : ''E'' → ''X'' satisfying <math>f \circ eq = g \circ eq</math>, | In more explicit terms, the equaliser consists of an object ''E'' and a morphism ''eq'' : ''E'' → ''X'' satisfying <math>f \circ eq = g \circ eq</math>, | ||
and such that, given any object ''O'' and morphism ''m'' : ''O'' → ''X'', if <math>f \circ m = g \circ m</math>, then there exists a [[unique (mathematics)|unique]] morphism ''u'' : ''O'' → ''E'' such that <math>eq \circ u = m</math>. | and such that, given any object ''O'' and morphism ''m'' : ''O'' → ''X'', if <math>f \circ m = g \circ m</math>, then there exists a [[unique (mathematics)|unique]] morphism ''u'' : ''O'' → ''E'' such that <math>eq \circ u = m</math>. | ||
A morphism <math>m:O \rightarrow X</math> is said to '''equalise''' <math>f</math> and <math>g</math> if <math>f \circ m = g \circ m</math>.<ref>{{cite book |last1=Barr |first1=Michael |author-link1=Michael Barr (mathematician) |last2=Wells |first2=Charles |author-link2=Charles Wells (mathematician) |year=1998 |title=Category theory for computing science |page=266 |url=http://www.math.mcgill.ca/triples/Barr-Wells-ctcs.pdf |access-date=2013-07-20 |format=PDF |archive-url=https://web.archive.org/web/20160304031956/http://www.math.mcgill.ca/triples/Barr-Wells-ctcs.pdf |archive-date=2016-03-04 |url-status=dead }}</ref> | |||
Revision as of 16:16, 28 June 2021
In more explicit terms, the equaliser consists of an object E and a morphism eq : E → X satisfying , and such that, given any object O and morphism m : O → X, if , then there exists a unique morphism u : O → E such that .
A morphism is said to equalise and if .[1]
- ↑ Barr, Michael; Wells, Charles (1998). Category theory for computing science (PDF). p. 266. Archived from the original (PDF) on 2016-03-04. Retrieved 2013-07-20. Unknown parameter
|url-status=ignored (help)