Geodesic
Small categories of homological dimension one
Theory and applications of categories, Tome 35 (2020), pp. 137-154 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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We derive three equivalent necessary conditions for a small category to have homological dimension one, generalizing a result of Novikov. As a consequence, any small cancellative category of homological dimension one is embeddable in a groupoid.

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Classification : 18G20, 20M50
Keywords: homological dimension, cohomological dimension, small category, cancellative category, cyclic system, crown, supported crown, DCC category, Malcev sequence, embeddability into a group 
@article{TAC_2020_35_a4,
     author = {Karimah Sweet and Charles Ching-An Cheng},
     title = {Small categories of homological dimension one},
     journal = {Theory and applications of categories},
     pages = {137--154},
     year = {2020},
     volume = {35},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a4/}
}
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Karimah Sweet; Charles Ching-An Cheng. Small categories of homological dimension one. Theory and applications of categories, Tome 35 (2020), pp. 137-154. http://geodesic.mathdoc.fr/item/TAC_2020_35_a4/