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Deductive systems and categories II. Standard constructions and closed categories

https://doi.org/10.1007/bfb0079385
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inferredcites →https://doi.org/10.1007/bf01703261openalex-snapshot
Deductive systems and categories

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Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Modal logics with n‐ary connectives
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Proof of a S.Mac Lane conjecture (extended abstract)
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Coherence for cartesian closed categories: A sequential approach
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What is a Logic, and What is a Proof?
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Normal Forms and Cut-Free Proofs as Natural Transformations
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Retracing Some Paths in Categorical Semantics: From Process-Propositions-as-Types to Categorified Reals and Computers
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Axiomatic Method and Category Theory
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Introduction
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New Axiomatic Method (Instead of Conclusion)
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Homotopical Categories of Logics
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General Framework
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Generalized Discontinuity
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Lambek Grammars with the Unit
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L-Models and R-Models for Lambek Calculus Enriched with Additives and the Multiplicative Unit
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What is a Logic, and What is a Proof?
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Deductive Systems and Categories in Linguistics
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Introduction
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Categorial and Categorical Grammars
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Coherence in cartesian closed categories and the generality of proofs
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Equality of maps and coherence theorem for biclosed categories
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The category of finite sets and Cartesian closed categories
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Closed categories and the theory of proofs
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Graded multicategories of polynomial-time realizers
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Toposes are monadic over categories
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Generalized Multicategories: Change-of-Base, Embedding, and Descent
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An Overview of Colax and Virtual Double Categories
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What is a Proof?
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The Displacement Calculus
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Grobner--Shirshov Bases, Conformal Algebras, and Pseudo-algebras
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Categorical interpretation of logical derivations and its applications in algebra
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Triples on functor categories
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Coherence in closed categories
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Languages for monoidal categories
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The structure of free closed categories
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An abstract framework for environment machines
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The History of Categorical Logic: 1963–1977
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\nOn the equivalence between Lurie's model and the dendroidal model for infinity-operads
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Irreducible modules over finite simple Lie pseudoalgebras I. Primitive pseudoalgebras of type W and S
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Coherence in linear predicate logic
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Feynman Graphs, and Nerve Theorem for Compact Symmetric Multicategories (Extended Abstract)
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Bifibrations of Polycategories and Classical Linear Logic
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Language models for some extensions of the Lambek calculus
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The categorical imperative: Category theory as a foundation for deontic logic
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Simple associative conformal algebras of linear growth
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Skew monoidal categories and skew multicategories
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Coherence for modalities
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Commutativity
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How strict is strictification?
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The logic of message-passing
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Monoidal indeterminates and categories of possible worlds
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On weak higher-dimensional categories I – 2
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Generalized enrichment of categories
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Relaxed multicategory structure of a global category of rings and modules
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Metric, topology and multicategory—a common approach
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Abstract substitution in enriched categories
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On weak higher dimensional categories I: Part 1
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General Logics
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Bibliography
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-algebras, -categories and -functors
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A monadic approach to polycategories
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Multiplicative Linear Logics and Fibrations
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Lambda-Calculus and Combinators in the 20th Century
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Bimonoids for Hyperplane Arrangements
inferred← citeshttps://doi.org/10.1017/9781108863117.001openalex-snapshot
Preface
inferred← citeshttps://doi.org/10.1017/9781108863117.002openalex-snapshot
Introduction
inferred← citeshttps://doi.org/10.1017/9781108863117.003openalex-snapshot
Species and operads
inferred← citeshttps://doi.org/10.1017/9781108863117.004openalex-snapshot
Hyperplane arrangements
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Species and bimonoids
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Bimonads on species
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Operads
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Basic theory of bimonoids
inferred← citeshttps://doi.org/10.1017/9781108863117.009openalex-snapshot
Primitive filtrations and decomposable filtrations
inferred← citeshttps://doi.org/10.1017/9781108863117.010openalex-snapshot
Universal constructions
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Examples of bimonoids
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Hadamard product
inferred← citeshttps://doi.org/10.1017/9781108863117.013openalex-snapshot
Exponential and logarithm
inferred← citeshttps://doi.org/10.1017/9781108863117.014openalex-snapshot
Characteristic operations
inferred← citeshttps://doi.org/10.1017/9781108863117.015openalex-snapshot
Modules over monoid algebras and bimonoids in species
inferred← citeshttps://doi.org/10.1017/9781108863117.016openalex-snapshot
Antipode
inferred← citeshttps://doi.org/10.1017/9781108863117.017openalex-snapshot
Structure theory for bimonoids
inferred← citeshttps://doi.org/10.1017/9781108863117.018openalex-snapshot
Loday–Ronco, Leray–Samelson, Borel–Hopf
inferred← citeshttps://doi.org/10.1017/9781108863117.019openalex-snapshot
Hoffman–Newman–Radford
inferred← citeshttps://doi.org/10.1017/9781108863117.020openalex-snapshot
Freeness under Hadamard products
inferred← citeshttps://doi.org/10.1017/9781108863117.021openalex-snapshot
Lie monoids
inferred← citeshttps://doi.org/10.1017/9781108863117.022openalex-snapshot
Poincaré–Birkhoff–Witt and Cartier–Milnor–Moore
inferred← citeshttps://doi.org/10.1017/9781108863117.023openalex-snapshot
Appendices
inferred← citeshttps://doi.org/10.1017/9781108863117.024openalex-snapshot
Vector spaces
inferred← citeshttps://doi.org/10.1017/9781108863117.025openalex-snapshot
Internal hom for monoidal categories
inferred← citeshttps://doi.org/10.1017/9781108863117.026openalex-snapshot
Higher monads
inferred← citeshttps://doi.org/10.1017/9781108863117.027openalex-snapshot
Author Index
inferred← citeshttps://doi.org/10.1017/9781108863117.028openalex-snapshot
Subject Index
inferred← citeshttps://doi.org/10.1017/s0305004112000394openalex-snapshot
Polynomial functors and polynomial monads
inferred← citeshttps://doi.org/10.1017/s0960129500000062openalex-snapshot
From Petri nets to linear logic
inferred← citeshttps://doi.org/10.1017/s0960129500000943openalex-snapshot
Hopf algebras and linear logic
inferred← citeshttps://doi.org/10.1017/s0960129500001055openalex-snapshot
! and ? – Storage as tensorial strength
inferred← citeshttps://doi.org/10.1017/s1446788700020334openalex-snapshot
Note on compact closed categories
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COMPLEXITY OF THE INFINITARY LAMBEK CALCULUS WITH KLEENE STAR
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Editorial Introduction
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Bicartesian Coherence
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The MacLane Problem on the Set-Theoretic Foundation for Category Theory. II
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A Local Two-Sorted Theory of Classes and Sets: MacLane's Problem and Mostowski's Program
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On Heisenberg-Virasoro pseudoalgebras
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Simplicial Endomorphisms
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The Tits–Kantor–Koecher Construction for Jordan Dialgebras
inferred← citeshttps://doi.org/10.1080/00927877508822067openalex-snapshot
Polycategories
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The Deduction Theorem (Before and After Herbrand)
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Trivalent logics arising from L-models for the Lambek calculus with constants
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A comparison between monoidal and substructural logics
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Topology and logic as a source of algebra
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Coherence in Nonmonoidal Closed Categories
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Towards a uniform presentation of logical systems by indexed categories and adjoint situations
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A substructural logic for layered graphs
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Shapely monads and analytic functors
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2-Dimensional Categories
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Copyright Page
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Dedication
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Preface
inferred← citeshttps://doi.org/10.1093/oso/9780198871378.002.0007openalex-snapshot
List of Main Facts
inferred← citeshttps://doi.org/10.1093/oso/9780198871378.002.0008openalex-snapshot
List of Notations
inferred← citeshttps://doi.org/10.1093/oso/9780198871378.003.0001openalex-snapshot
Categories
inferred← citeshttps://doi.org/10.1093/oso/9780198871378.003.0002openalex-snapshot
Bicategories and 2-Categories
inferred← citeshttps://doi.org/10.1093/oso/9780198871378.003.0003openalex-snapshot
Pasting Diagrams
inferred← citeshttps://doi.org/10.1093/oso/9780198871378.003.0004openalex-snapshot
Functors, Transformations, and Modifications
inferred← citeshttps://doi.org/10.1093/oso/9780198871378.003.0005openalex-snapshot
Bicategorical Limits and Nerves
inferred← citeshttps://doi.org/10.1093/oso/9780198871378.003.0006openalex-snapshot
Adjunctions and Monads
inferred← citeshttps://doi.org/10.1093/oso/9780198871378.003.0007openalex-snapshot
The Whitehead Theorem for Bicategories
inferred← citeshttps://doi.org/10.1093/oso/9780198871378.003.0008openalex-snapshot
The Yoneda Lemma and Coherence
inferred← citeshttps://doi.org/10.1093/oso/9780198871378.003.0009openalex-snapshot
Grothendieck Fibrations
inferred← citeshttps://doi.org/10.1093/oso/9780198871378.003.0010openalex-snapshot
The Grothendieck Construction
inferred← citeshttps://doi.org/10.1093/oso/9780198871378.003.0011openalex-snapshot
The Tricategory of Bicategories
inferred← citeshttps://doi.org/10.1093/oso/9780198871378.003.0012openalex-snapshot
Further 2-Dimensional Categorical Structures
inferred← citeshttps://doi.org/10.1098/rsta.2018.0038openalex-snapshot
The problem of proof identity, and why computer scientists should care about Hilbert's 24th problem
inferred← citeshttps://doi.org/10.1109/lics65433.2025.00014openalex-snapshot
On the denotation of circular and non-wellfounded proofs in linear logic with fixed points
inferred← citeshttps://doi.org/10.1112/plms/pdp034openalex-snapshot
Localization of algebras over coloured operads
inferred← citeshttps://doi.org/10.1142/11626openalex-snapshot
Homotopical Quantum Field Theory
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