### Separable morphisms of simplicial sets.

Chikhladze, Dimitri (2006)

Journal of Homotopy and Related Structures

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Chikhladze, Dimitri (2006)

Journal of Homotopy and Related Structures

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Janelidze, G., Kelly, G.M. (1997)

Theory and Applications of Categories [electronic only]

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Isbell, J. R.

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Tholen, Walter (1999)

Homology, Homotopy and Applications

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J. N. Alonso Alvarez, J. M. Fernandez Vilaboa (1994)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Hofstra, Pieter, De Marchi, Federico (2006)

Theory and Applications of Categories [electronic only]

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C. Castellini, J. Koslowski, G. E. Strecker (1994)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Lawvere, F.William (2007)

Theory and Applications of Categories [electronic only]

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Marco Riccardi (2013)

Formalized Mathematics

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Category theory was formalized in Mizar with two different approaches [7], [18] that correspond to those most commonly used [16], [5]. Since there is a one-to-one correspondence between objects and identity morphisms, some authors have used an approach that does not refer to objects as elements of the theory, and are usually indicated as object-free category [1] or as arrowsonly category [16]. In this article is proposed a new definition of an object-free category, introducing the two...