11 citations · 72 across the 39 of their papers we have counts for
19 papers · 1 filter
Weak Cat-Operads
Kosta DOSEN, Zoran Petric
An operad (this paper deals with non-symmetric operads)may be conceived as a partial algebra with a family of insertion operations, Gerstenhaber's circle-i products, which satisfy…
Coherence for Monoidal Monads and Comonads
K. Dosen, Z. Petric
The goal of this paper is to prove coherence results with respect to relational graphs for monoidal monads and comonads, i.e. monads and comonads in a monoidal category such that t…
Coherence for Monoidal Endofunctors
K. Dosen, Z. Petric
The goal of this paper is to prove coherence results with respect to relational graphs for monoidal endofunctors, i.e. endofunctors of a monoidal category that preserve the monoida…
Syntax for Split Preorders
K. Dosen, Z. Petric
A split preorder is a preordering relation on the disjoint union of two sets, which function as source and target when one composes split preorders. The paper presents by generator…
Ordinals in Frobenius Monads
K. Dosen, Z. Petric
This paper provides geometrical descriptions of the Frobenius monad freely generated by a single object. These descriptions are related to results connecting Frobenius algebras and…
Bicartesian Coherence Revisited
K. Dosen, Z. Petric
A survey is given of results about coherence for categories with finite products and coproducts. For these results, which were published previously by the authors in several places…
Intermutation
K. Dosen, Z. Petric
This paper proves coherence results for categories with a natural transformation called \emph{intermutation} made of arrows from to ${(A\vee C)\wedge(B…
Medial Commutativity
K. Dosen, Z. Petric
It is shown that all the assumptions for symmetric monoidal categories flow out of a unifying principle involving natural isomorphisms of the type ${(A\otimes B)\otimes(C\otimes D)…
Symmetric Self-Adjunctions and Matrices
K. Dosen, Z. Petric
It is shown that the multiplicative monoids of Brauer's centralizer algebras generated out of the basis are isomorphic to monoids of endomorphisms in categories where an endofuncto…
Coherence and Confluence
K. Dosen, Z. Petric
Proofs of coherence in category theory, starting from Mac Lane's original proof of coherence for monoidal categories, are sometimes based on confluence techniques analogous to what…
Associativity as Commutativity
K. Dosen, Z. Petric
It is shown that coherence conditions for monoidal categories concerning associativity are analogous to coherence conditions for symmetric or braided strictly monoidal categories,…
Relevant Categories and Partial Functions
K. Dosen, Z. Petric
A relevant category is a symmetric monoidal closed category with a diagonal natural transformation that satisfies some coherence conditions. Every cartesian closed category is a re…
Coherence for Star-Autonomous Categories
K. Dosen, Z. Petric
This paper presents a coherence theorem for star-autonomous categories exactly analogous to Kelly's and Mac Lane's coherence theorem for symmetric monoidal closed categories. The p…
Coherence of Proof-Net Categories
K. Dosen, Z. Petric
The notion of proof-net category defined in this paper is closely related to graphs implicit in proof nets for the multiplicative fragment without constant propositions of linear l…
Abstraction and Application in Adjunction
K. Dosen
The postulates of comprehension and extensionality in set theory are based on an inversion principle connecting set-theoretic abstraction and the property of having a member. An ex…
Coherent Bicartesian and Sesquicartesian Categories
K. Dosen, Z. Petric
Coherence is here demonstrated for sesquicartesian categories, which are categories with nonempty finite products and arbitrary finite sums, including the empty sum, where moreover…
Bicartesian Coherence
K. Dosen, Z. Petric
Coherence is demonstrated for categories with binary products and sums, but without the terminal and the initial object, and without distribution. This coherence amounts to the exi…
The Maximality of Cartesian Categories
Kosta Dosen, Zoran Petric
It is proved that equalities between arrows assumed for cartesian categories are maximal in the sense that extending them with any new equality in the language of free cartesian ca…
The Maximality of the Typed Lambda Calculus and of Cartesian Closed Categories
Kosta Dosen, Zoran Petric
From the analogue of Boehm's Theorem proved for the typed lambda calculus, without product types and with them, it is inferred that every cartesian closed category that satisfies a…