Ehresmann, Andrée C. Colimits in free categories. (English) Zbl 0919.18002 Diagrammes 37, 3-12 (1997). This paper characterizes diagrams admitting a colimit in a category with diagonals. Since free categories and groupoids are such categories, the above characterization naturally leads to specific results in these special categories. The author discusses a possible application of much interest in biology and neurology, in which the formation of higher order objects is allegedly represented by a completion process. Reviewer: Hirokazu Nishimura (Tsukuba) MSC: 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories) 92B99 Mathematical biology in general Keywords:groupoids; neurology; colimit; category with diagonals × Cite Format Result Cite Review PDF Full Text: EuDML References: [1] 1. Bienenstock, E. & von der Malsburg, C., Statistical coding and short-term synaptic plasticity, in Disordered systems and biological organization, NATO NASI Series 20, Springer, 1986. MR846215 · Zbl 1325.92022 [2] 2. Ehresmann, A.C. & Vanbremeersch, J.-P., Outils mathématiques pour modéliser les systèmes complexes, Cahiers Top. et Géom. Diff. Cat. XXXIII-3 ( 1992), 225-236. Zbl0766.92001 MR1186947 · Zbl 0766.92001 [3] 3. Ehresmann, A.C. & Vanbremeersch, J.-P., Multiplicity Principle and Emergence in Memory Evolutive Systems, J. of Systems Analysis, Modelling, Simulation 26 ( 1996), 81-117. Zbl0879.92001 · Zbl 0879.92001 [4] 4. Ehresmann, A.C. & Vanbremeersch, J.-P., Hierarchical Evolutive Systems, in Proceedings 8th international conference of Cybernetics and Systems, New York 1990, Vol. 1, The NIJT Press, Newark, 1991, 320-327. · Zbl 0619.92001 [5] 5. Lair, C., Sur le genre d’esquissabilité des catégories modelables (accessibles) possédant les produits de deux, Diagrammes 35, Paris, 1996. Zbl0899.18003 · Zbl 0899.18003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.