### From cubical to globular higher categories

Marco Grandis, Robert Paré (2012)

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Marco Grandis, Robert Paré (2012)

Diagrammes

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Jan Jastrzębski (1983)

Fundamenta Mathematicae

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Mara Alagić (1989)

Publications de l'Institut Mathématique

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Julia E. Bergner, Philip Hackney (2015)

Fundamenta Mathematicae

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We study a certain type of action of categories on categories and on operads. Using the structure of the categories Δ and Ω governing category and operad structures, respectively, we define categories which instead encode the structure of a category acting on a category, or a category acting on an operad. We prove that the former has the structure of an elegant Reedy category, whereas the latter has the structure of a generalized Reedy category. In particular, this approach gives a new...

Mara Alagić (1991)

Publications de l'Institut Mathématique

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Hans-Jürgen Vogel (2003)

Discussiones Mathematicae - General Algebra and Applications

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The categorical concept of a theory for algebras of a given type was foundet by Lawvere in 1963 (see [8]). Hoehnke extended this concept to partial heterogenous algebras in 1976 (see [5]). A partial theory is a dhts-category such that the object class forms a free algebra of type (2,0,0) freely generated by a nonempty set J in the variety determined by the identities ox ≈ o and xo ≈ o, where o and i are the elements selected by the 0-ary operation symbols. If the object class of a dhts-category...

Jakobsen, Per K., Lychagin, Valentin V. (2005)

Lobachevskii Journal of Mathematics

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G. M. Kelly (1986)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Lack, Stephen (2007)

Theory and Applications of Categories [electronic only]

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Andrée Ehresmann, Charles Ehresmann (1978)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Andrée Bastiani, Charles Ehresmann (1974)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Marco Riccardi (2015)

Formalized Mathematics

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The main purpose of this article is to introduce the categorical concept of pullback in Mizar. In the first part of this article we redefine homsets, monomorphisms, epimorpshisms and isomorphisms [7] within a free-object category [1] and it is shown there that ordinal numbers can be considered as categories. Then the pullback is introduced in terms of its universal property and the Pullback Lemma is formalized [15]. In the last part of the article we formalize the pullback of functors...