Geodesic
On the Limitations of Sketches
Canadian mathematical bulletin, Tome 35 (1992) no. 3, pp. 287-294

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DOI

Call a category "sketchable" if it is the category of models in sets of some sketch. This paper explores the subtle boundary between sketchable and non-sketchable categories. We show that the category of small categories that have at least one initial object and functors that take an initial object to an initial object is sketchable. The same is true for weak initial objects, but is false for subinitial objects (that every object has at most one arrow to). Analogous results hold if we substitute finite limits for terminal object. We also show that the category of groups and center-preserving homomorphisms is not sketchable. We describe briefly how "higher-order" sketches can fill these gaps.
DOI : 10.4153/CMB-1992-040-7
Mots-clés : 18C10, 18A10, accessible categories, regular categories, embeddings 
Barr, Michael; Wells, Charles. On the Limitations of Sketches. Canadian mathematical bulletin, Tome 35 (1992) no. 3, pp. 287-294. doi: 10.4153/CMB-1992-040-7
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     doi = {10.4153/CMB-1992-040-7},
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