A construction of certain weak colimits and an exactness property of the 2-category of categories
Given a 2-category A, a 2-functor A (Formula Presented) Cat and a distinguished 1-subcategory Σ ⊂ A containing all the objects, a σ-cone for F (with respect to Σ) is a lax cone such that the structural 2-cells corresponding to the arrows of Σ are invertible. The conical σ-limit is the universal (up...
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Mount Allison University
2018
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| LEADER | 04613caa a22004937a 4500 | ||
|---|---|---|---|
| 001 | PAPER-25236 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518205715.0 | ||
| 008 | 190410s2018 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-85044729476 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Descotte, M.E. | |
| 245 | 1 | 2 | |a A construction of certain weak colimits and an exactness property of the 2-category of categories |
| 260 | |b Mount Allison University |c 2018 | ||
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Artin, M., Grothendieck, A., Verdier, J., SGA 4, Ch VII, (1963-64) (1972) Springer Lecture Notes in Mathematics, p. 270 | ||
| 504 | |a Canevali, N., (2016) 2-Filtered Bicolimits and Finite Weighted Bilimits Commute in Cat, , http://cms.dm.uba.ar/academico/carreras/licenciatura/tesis/, degree thesis, 2016 | ||
| 504 | |a Data, M.I., (2014) Una construcción De bicolímites 2-Filtrantes De categorías, , http://cms.dm.uba.ar/academico/carreras/licenciatura/tesis/2014, degree thesis | ||
| 504 | |a Descotte, M.E., Dubuc, E.J., Szyld, M., (2017) On the Notion of Flat 2-Functors | ||
| 504 | |a Dubuc, E.J., Street, R., A construction of 2-filtered bicolimits of categories (2006) Cahiers De Topologie Et Géométrie Différentielle Catégoriques, 47 (2), pp. 83-106 | ||
| 504 | |a Gray, J.W., Formal category theory: Adjointness for 2-categories (1974) Springer Lecture Notes in Mathematics, p. 391 | ||
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| 504 | |a Kelly, G.M., Elementary observations on 2-Categorical limits (1989) Bull. Austral. Math. Soc, 39, pp. 301-317 | ||
| 504 | |a Kelly, G.M., Street, R., Review of the elements of 2-categories (1974) Springer Lecture Notes in Mathematics, 420, pp. 75-103 | ||
| 504 | |a Kennison, J., The fundamental localic groupoid of a topos (1992) Journal of Pure and Applied Algebra, 77, pp. 67-86 | ||
| 504 | |a Pronk, D.A., Etendues and stacks as bicategories of fractions (1996) Compositio Mathematica, 102 (3), pp. 243-303 | ||
| 504 | |a Street, R., Fibrations in bicategories (1980) Cahiers De Topologie Et géométrie différentielle catégoriques, 21 (2), pp. 111-160 | ||
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| 520 | 3 | |a Given a 2-category A, a 2-functor A (Formula Presented) Cat and a distinguished 1-subcategory Σ ⊂ A containing all the objects, a σ-cone for F (with respect to Σ) is a lax cone such that the structural 2-cells corresponding to the arrows of Σ are invertible. The conical σ-limit is the universal (up to isomorphism) σ-cone. The notion of σ-limit generalizes the well known notions of pseudo and lax limit. We consider the fundamental notion of σ-filtered pair (A, Σ) which generalizes the notion of 2-filtered 2-category. We give an explicit construction of σ-filtered σ-colimits of categories, a construction which allows computations with these colimits. We then state and prove a basic exactness property of the 2-category of categories, namely, that σ-filtered σ-colimits commute with finite weighted pseudo (or bi) limits. An important corollary of this result is that a σ-filtered σ-colimit of exact category valued 2-functors is exact. This corollary is essential in the 2-dimensional theory of flat and pro-representable 2-functors, that we develop elsewhere. © Descotte M.E., Dubuc E.J., Szyld M., 2018. |l eng | |
| 593 | |a LaBRI, Université de Bordeaux, France | ||
| 593 | |a IMAS, Universidad de Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a 2-CATEGORY |
| 690 | 1 | 0 | |a EXACTNESS PROPERTY |
| 690 | 1 | 0 | |a FILTERED |
| 690 | 1 | 0 | |a WEAK COLIMIT |
| 700 | 1 | |a Dubuc, E.J. | |
| 700 | 1 | |a Szyld, M. | |
| 773 | 0 | |d Mount Allison University, 2018 |g v. 33 |h pp. 193-215 |p Theory Appl. Categories |x 1201561X |w (AR-BaUEN)CENRE-8784 |t Theory and Applications of Categories | |
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| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_1201561X_v33_n_p193_Descotte |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1201561X_v33_n_p193_Descotte |y Registro en la Biblioteca Digital |
| 961 | |a paper_1201561X_v33_n_p193_Descotte |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||
| 999 | |c 86189 | ||