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Journal articles on the topic 'Limits and colimits'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

COCKETT, ROBIN, and STEPHEN LACK. "Restriction categories III: colimits, partial limits and extensivity." Mathematical Structures in Computer Science 17, no. 4 (2007): 775–817. http://dx.doi.org/10.1017/s0960129507006056.

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A restriction category is an abstract formulation for a category of partial maps, defined in terms of certain specified idempotents called the restriction idempotents. All categories of partial maps are restriction categories; conversely, a restriction category is a category of partial maps if and only if the restriction idempotents split. Restriction categories facilitate reasoning about partial maps as they have a purely algebraic formulation.In this paper we consider colimits and limits in restriction categories. As the notion of restriction category is not self-dual, we should not expect c

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2

Khoshkam, M., and J. Tavakoli. "Categorical constructions in C*-algebra theory." Journal of the Australian Mathematical Society 73, no. 1 (2002): 97–114. http://dx.doi.org/10.1017/s1446788700008491.

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AbstractThe notions of limits and colimits are studied in the category of C*-algebras. It is shown that limits and colimits of diagrams of C*-algebras are stable under tensor product by a fixed C*-algebra, and crossed product by a locally compact group.

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3

Porst, Hans-E. "Limits and colimits of Hopf algebras." Journal of Algebra 328, no. 1 (2011): 254–67. http://dx.doi.org/10.1016/j.jalgebra.2010.10.014.

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4

Adámek, Jiří, and Jiří Rosický. "Finitary sketches and finitely accessible categories." Mathematical Structures in Computer Science 5, no. 3 (1995): 315–22. http://dx.doi.org/10.1017/s0960129500000773.

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Every accessible category is proved to be sketchable by a sketch with finite colimits. In contrast, a finitely accessible category is presented that cannot be sketched by a finitary sketch, i.e., a sketch with finite limits and finite colimits. Also, a category sketchable by a finitary sketch is found that is not finitely accessible.

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5

Isaksen, Daniel C. "Calculating limits and colimits in pro-categories." Fundamenta Mathematicae 175, no. 2 (2002): 175–94. http://dx.doi.org/10.4064/fm175-2-7.

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6

Vokřínek, Lukáš. "Pushouts of Categories, Derived Limits, and Colimits." Communications in Algebra 44, no. 5 (2016): 2110–17. http://dx.doi.org/10.1080/00927872.2015.1033718.

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7

Saengsura, K. "LIMITS AND COLIMITS OF (F_1, F_2)-SYSTEMS." Far East Journal of Mathematical Sciences (FJMS) 102, no. 11 (2017): 2845–60. http://dx.doi.org/10.17654/ms102112845.

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8

Chollet, Emma, Bryce Clarke, Michael Johnson, Maurine Songa, Vincent Wang, and Gioele Zardini. "Limits and Colimits in a Category of Lenses." Electronic Proceedings in Theoretical Computer Science 372 (November 1, 2022): 164–77. http://dx.doi.org/10.4204/eptcs.372.12.

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9

Solovyov, Sergey A. "On limits and colimits of variety-based topological systems." Fuzzy Sets and Systems 178, no. 1 (2011): 54–73. http://dx.doi.org/10.1016/j.fss.2011.04.002.

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10

HÉBERT, M., and J. ROSICKÝ. "UNCOUNTABLE ORTHOGONALITY IS A CLOSURE PROPERTY." Bulletin of the London Mathematical Society 33, no. 6 (2001): 685–88. http://dx.doi.org/10.1112/s0024609301008451.

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It is shown that, for λ > ω, λ-orthogonality classes in locally λ-presentable categories coincide with full subcategories that are closed under limits and under λ-directed colimits. This comes as a surprise, since the statement is known to be false for λ = ω.

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11

Hu, Hongde. "Flat functors and free exact categories." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 60, no. 2 (1996): 143–56. http://dx.doi.org/10.1017/s1446788700037575.

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AbstractLet C be a small category with weak finite limits, and let Flat(C) be the category of flat functors from C to the category of small sets. We prove that the free exact completion of C is the category of set-valued functors of Flat (C) which preserve small products and filtered colimits. In case C has finite limits, this gives A. Carboni and R. C. Magno's result on the free exact completion of a small category with finite limits.

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12

Beattie, R., and H. P. Butzmann. "Continuous Duality of Limits and Colimits of Topological Abelian Groups." Applied Categorical Structures 16, no. 4 (2007): 535–49. http://dx.doi.org/10.1007/s10485-007-9112-5.

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13

Riehl, Emily, and Dominic Verity. "Recognizing Quasi-Categorical Limits and Colimits in Homotopy Coherent Nerves." Applied Categorical Structures 28, no. 4 (2020): 669–716. http://dx.doi.org/10.1007/s10485-020-09594-x.

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14

Orlicki, Andrzej. "Computable limits and colimits in categories of partial enumerated sets." Mathematical Logic Quarterly 39, no. 1 (1993): 181–96. http://dx.doi.org/10.1002/malq.19930390121.

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15

Ebrahimi, M. M., and M. Mahmoudi. "CATEGORY OF M-ALGEBRAS AND INTERNAL HOMOMORPHISMS." Asian-European Journal of Mathematics 03, no. 02 (2010): 307–22. http://dx.doi.org/10.1142/s1793557110000210.

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Recall that for (universal) algebras A and B in a category [Formula: see text], [Formula: see text] is usually an external object, in the sense that it is just a set and is neither an algebra nor an (internal) object of the base category [Formula: see text]. Ebrahimi introduced an object [A, B] inside [Formula: see text] to be the best counterpart of Hom(A, B), for universal algebras A, B in a Grothendieck topos [Formula: see text]. In this paper, taking a monoid M and an equational category of algebras [Formula: see text], we introduce the category [Formula: see text] of universal algebras in

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16

Power, A. J., and Charles Wells. "A formalism for the specification of essentially-algebraic structures in 2-categories." Mathematical Structures in Computer Science 2, no. 1 (1992): 1–28. http://dx.doi.org/10.1017/s0960129500001110.

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A type of higher-order two-dimensional sketch is defined which has models in suitable 2-categories. It has as special cases the ordinary sketches of Ehresmann and certain previously defined generalizations of one-dimensional sketches. These sketches allow the specification of constructions in 2-categories such as weighted limits, as well as higher-order constructions such as exponential objects and subobject classifiers, that cannot be sketched by limits and colimits. These sketches are designed to be the basis of a category-based methodology for the description of functional programming langu

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17

Shahbaz, Leila. "Injective and projective poset acts." Quasigroups and Related Systems 31, no. 1(49) (2023): 152–64. http://dx.doi.org/10.56415/qrs.v31.11.

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In this paper, after recalling the category {\bf PosAct}-$S$ of all poset acts over a pomonoid $S$; an $S$-act in the category {\bf Pos} of all posets, with action preserving monotone maps between them, some categorical properties of the category {\bf PosAct}-$S$ are considered. In particular, we describe limits and colimits such as products, coproducts, equalizers, coequalizers and etc. in this category. Also, several kinds of epimorphisms and monomorphisms are characterized in {\bf PosAct}-$S$. Finally, we study injectivity and projectivity in {\bf PosAct}-$S$ with respect to (regular) monom

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18

Hogle, Shane L., Christopher L. Dupont, Brian M. Hopkinson, et al. "Pervasive iron limitation at subsurface chlorophyll maxima of the California Current." Proceedings of the National Academy of Sciences 115, no. 52 (2018): 13300–13305. http://dx.doi.org/10.1073/pnas.1813192115.

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Subsurface chlorophyll maximum layers (SCMLs) are nearly ubiquitous in stratified water columns and exist at horizontal scales ranging from the submesoscale to the extent of oligotrophic gyres. These layers of heightened chlorophyll and/or phytoplankton concentrations are generally thought to be a consequence of a balance between light energy from above and a limiting nutrient flux from below, typically nitrate (NO3). Here we present multiple lines of evidence demonstrating that iron (Fe) limits or with light colimits phytoplankton communities in SCMLs along a primary productivity gradient fro

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19

Ion, C. Baianu, Georgescu George, F. Glazebrook James, and Brown Ronald. "BRAIN Journal - Lukasiewicz-Moisil Many-Valued Logic Algebra of Highly-Complex Systems." Brain Journal 1, SPECIAL ISSUE ON COMPLEXITY IN SCIENCES AND ARTIFICIAL INTELLIGENCE (2010): 1–11. https://doi.org/10.5281/zenodo.1037321.

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ABSTRACT The fundamentals of ÃLukasiewicz-Moisil logic algebras and their applications to complex genetic network dynamics and highly complex systems are presented in the context of a categorical ontology theory of levels, Medical Bioinformatics and self-organizing, highly complex systems. Quantum Automata were defined in refs.[2] and [3] as generalized, probabilistic automata with quantum state spaces [1]. Their next-state functions operate through transitions between quantum states defined by the quantum equations of motions in the Schr¨odinger representation, with both initial and boundary

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20

Mesablishvili, Bachuki, and Robert Wisbauer. "Bimonads and Hopf monads on categories." Journal of K-Theory 7, no. 2 (2010): 349–88. http://dx.doi.org/10.1017/is010001014jkt105.

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AbstractThe purpose of this paper is to develop a theory of bimonads and Hopf monads on arbitrary categories thus providing the possibility to transfer the essentials of the theory of Hopf algebras in vector spaces to more general settings. There are several extensions of this theory to monoidal categories which in a certain sense follow the classical trace. Here we do not pose any conditions on our base category but we do refer to the monoidal structure of the category of endofunctors on any category and by this we retain some of the combinatorial complexity which makes the theory so interest

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21

KOSTANEK, MATEUSZ, and PAWEŁ WASZKIEWICZ. "The limit–colimit coincidence theorem for -categories." Mathematical Structures in Computer Science 20, no. 2 (2010): 267–84. http://dx.doi.org/10.1017/s0960129509990387.

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We prove that the category of-cocomplete separated-categories has bilimits of expanding sequences. This result generalises on various levels the well-known theorem of domain theory that guarantees the existence of bilimits in the category of directed-complete posets and Scott-continuous maps.

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22

Liang, Shaohui. "Algebraic Properties of the Category of Involutive m-Semilattices and Its Limits." Symmetry 17, no. 7 (2025): 1051. https://doi.org/10.3390/sym17071051.

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An involutive m-semilattice is a kind of algebraic structure with symmetry. Symmetry is reflected from partial-order relations to algebraic operations and even categorical properties. In this study, firstly, the concepts of the nucleus and congruence in involutive m-semilattices are introduced, and their interrelationships are discussed. On this basis, the concrete structure of a coequalizer in the category of involutive m-semilattices is obtained. We introduce the definition of free involutive m-semilattices, and the concrete structure of involutive m-semilattices is discussed. In addition, I

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23

Aratake, Hisashi. "Limits, Colimits, and Spectra of Modelled Spaces." Journal of Pure and Applied Algebra, May 2023, 107414. http://dx.doi.org/10.1016/j.jpaa.2023.107414.

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24

Miranda, Adrian. "Enriched Kleisli Objects for Pseudomonads." Applied Categorical Structures 33, no. 4 (2025). https://doi.org/10.1007/s10485-025-09810-6.

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Abstract A pseudomonad on a 2-category whose underlying endomorphism is a 2-functor can be seen as a diagram $$\textbf{Psmnd} \rightarrow \textbf{Gray}$$ Psmnd → Gray for which weighted limits and colimits can be considered. The 2-category of pseudoalgebras, pseudomorphisms and 2-cells is such a Gray-enriched weighted limit [21], however neither the Kleisli bicategory nor the 2-category of free pseudoalgebras are the analogous weighted colimit [13]. In this paper we describe the actual weighted colimit via a presentation, and show that the comparison 2-functor induced by any other pseudoadjunc

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25

Salati, Edoardo. "Limits and colimits, generators and relations of partial groups." Journal of Algebra, February 2023. http://dx.doi.org/10.1016/j.jalgebra.2023.01.014.

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26

Positselski, Leonid. "Flat comodules and contramodules as directed colimits, and cotorsion periodicity." Journal of Homotopy and Related Structures, October 9, 2024. http://dx.doi.org/10.1007/s40062-024-00358-1.

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AbstractThis paper is a follow-up to Positselski and Št’ovíček (Flat quasi-coherent sheaves as directed colimits, and quasi-coherent cotorsion periodicity. Electronic preprint arXiv:2212.09639 [math.AG]). We consider two algebraic settings of comodules over a coring and contramodules over a topological ring with a countable base of two-sided ideals. These correspond to two (noncommutative) algebraic geometry settings of certain kind of stacks and ind-affine ind-schemes. In the context of a coring $${\mathcal {C}}$$ C over a noncommutative ring A, we show that all A-flat $${\mathcal {C}}$$ C -c

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27

Pasqualetto, Enrico. "Limits and colimits in the category of Banach $L^{0}$-modules." Rendiconti del Seminario Matematico della Università di Padova, May 29, 2024. http://dx.doi.org/10.4171/rsmup/163.

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28

Tendas, Giacomo. "Flatness, weakly lex colimits, and free exact completions." Annali di Matematica Pura ed Applicata (1923 -), October 5, 2023. http://dx.doi.org/10.1007/s10231-023-01383-2.

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AbstractWe capture in the context of lex colimits, introduced by Garner and Lack, the universal property of the free regular and Barr-exact completions of a weakly lex category. This is done by introducing a notion of flatness for functors $$F:{{\mathcal {C}}}\rightarrow {{\mathcal {E}}}$$ F : C → E with lex codomain, and using this to describe the universal property of free $$\Phi $$ Φ -exact completions in the absence of finite limits, for any given class $$\Phi $$ Φ of lex weights. In particular, we shall give necessary and sufficient conditions for the existence of free lextensive and free

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29

Gambino, Nicola, Simon Henry, Christian Sattler, and Karol Szumiło. "The effective model structure and -groupoid objects." Forum of Mathematics, Sigma 10 (2022). http://dx.doi.org/10.1017/fms.2022.13.

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Abstract For a category $\mathcal {E}$ with finite limits and well-behaved countable coproducts, we construct a model structure, called the effective model structure, on the category of simplicial objects in $\mathcal {E}$ , generalising the Kan–Quillen model structure on simplicial sets. We then prove that the effective model structure is left and right proper and satisfies descent in the sense of Rezk. As a consequence, we obtain that the associated $\infty $ -category has finite limits, colimits satisfying descent, and is locally Cartesian closed when $\mathcal {E}$ is but is not a higher t

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30

Flaten, Jarl G. Taxerås. "Univalent categories of modules." Mathematical Structures in Computer Science, June 23, 2023, 1–28. http://dx.doi.org/10.1017/s0960129523000178.

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Abstract We show that categories of modules over a ring in homotopy type theory (HoTT) satisfy the internal versions of the AB axioms from homological algebra. The main subtlety lies in proving AB4, which is that coproducts indexed by arbitrary sets are left-exact. To prove this, we replace a set X with the strict category of lists of elements in X. From showing that the latter is filtered, we deduce left-exactness of the coproduct. More generally, we show that exactness of filtered colimits (AB5) implies AB4 for any abelian category in HoTT. Our approach is heavily inspired by Roswitha Hartin

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31

Baker, Matthew, Tong Jin, and Oliver Lorscheid. "New building blocks for F1${\mathbb {F}}_1$‐geometry: Bands and band schemes." Journal of the London Mathematical Society 111, no. 4 (2025). https://doi.org/10.1112/jlms.70125.

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AbstractWe develop and study a generalization of commutative rings called bands, along with the corresponding geometric theory of band schemes. Bands generalize both hyperrings, in the sense of Krasner, and partial fields in the sense of Semple and Whittle. They form a ring‐like counterpart to the field‐like category of idylls introduced by the first and third authors in the previous work. The first part of the paper is dedicated to establishing fundamental properties of bands analogous to basic facts in commutative algebra. In particular, we introduce various kinds of ideals in a band and exp

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32

Ximenes, Martins Yuri, and Biezuner Rodney Josué. "On Extensions of Yang-Mills-Type Theories, Their Spaces and Their Categories." July 24, 2020. https://doi.org/10.5281/zenodo.3959688.

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In this paper we consider the classification problem of extensions of Yang-Mills-type (YMT) theories. For us, a YMT theory differs from the classical Yang-Mills theories by allowing an arbitrary pairing on the curvature. The space of YMT theories with a prescribed gauge group G and instanton sector P is classified, an upper bound to its rank is given and it is compared with the space of Yang-Mills theories. We present extensions of YMT theories as a simple and unified approach to many different notions of deformations and addition of correction terms previously discussed in

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33

Kim, JiHyun, Yeonjoo Kim, Donatella Zona, et al. "Carbon response of tundra ecosystems to advancing greenup and snowmelt in Alaska." Nature Communications 12, no. 1 (2021). http://dx.doi.org/10.1038/s41467-021-26876-7.

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AbstractThe ongoing disproportionate increases in temperature and precipitation over the Arctic region may greatly alter the latitudinal gradients in greenup and snowmelt timings as well as associated carbon dynamics of tundra ecosystems. Here we use remotely-sensed and ground-based datasets and model results embedding snowmelt timing in phenology at seven tundra flux tower sites in Alaska during 2001–2018, showing that the carbon response to early greenup or delayed snowmelt varies greatly depending upon local climatic limits. Increases in net ecosystem productivity (NEP) due to early greenup

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34

Held, Noelle A., Aswin Krishna, Donat Crippa, et al. "Nutrient colimitation is a quantitative, dynamic property of microbial populations." Proceedings of the National Academy of Sciences 121, no. 52 (2024). https://doi.org/10.1073/pnas.2400304121.

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Resource availability dictates how fast and how much microbial populations grow. Quantifying the relationship between microbial growth and resource concentrations makes it possible to promote, inhibit, and predict microbial activity. Microbes require many resources, including macronutrients (e.g., carbon and nitrogen), micronutrients (e.g., metals), and complex nutrients like vitamins and amino acids. When multiple resources are scarce, as frequently occurs in nature, microbes may experience resource colimitation in which more than one resource simultaneously limits growth. Despite growing evi

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